Excitation of bond-alternating spin-1/2 Heisenberg chains by tunnelling electrons.
Gauyacq, J-P; Lorente, N
2014-10-01
Inelastic electron tunneling spectra (IETS) are evaluated for spin-1/2 Heisenberg chains showing different phases of their spin ordering. The spin ordering is controlled by the value of the two different Heisenberg couplings on the two sides of each of the chain's atoms (bond-alternating chains). The perfect anti-ferromagnetic phase, i.e. a unique exchange coupling, marks a topological quantum phase transition (TQPT) of the bond-alternating chain. Our calculations show that the TQPT is recognizable in the excited states of the chain and hence that IETS is in principle capable of discriminating the phases. We show that perfectly symmetric chains, such as closed rings mimicking infinite chains, yield the same spectra on both sides of the TQPT and IETS cannot reveal the nature of the spin phase. However, for finite size open chains, both sides of the TQPT are associated with different IETS spectra, especially on the edge atoms, thus outlining the transition.
Liu, Bo; Xue, Kang; Wang, Gangcheng
2016-12-01
In this paper, we investigate the four-qubit spin-1/2 XXZ Heisenberg chain with Dzyaloshinskii-Moriya interaction by topological basis method, and research the relationship between the topological basis states and the ground states. In order to study the Hamiltonian system beyond XXZ model, we introduce two Temperley-Lieb algebra generators and two other generalized generators. Then we investigate the relationship between topological basis and Heisenberg XXZ model with Dzyaloshinskii-Moriya interaction. The results show that the ground state of this model falls on the topological basis state for anti-ferromagnetic case and gapless phase case.
Entanglement oscillations in open Heisenberg chains
Wang, T; Wang, X; Sun, Zhe; Wang, Ting; Wang, Xiaoguang
2006-01-01
We study pairwise entanglements in spin-half and spin-one Heisenberg chains with an open boundary condition, respectively. We find out that the ground-state and the first-excited-state entanglements are equal for the three-site spin-one chain. When the number of sites L>3, the concurrences and negativities display oscillatory behaviors, and the oscillations of the ground-state and the first-excited-state entanglements are out of phase or in phase.
Entanglement in spin-one Heisenberg chains
Wang, X G; Sun, Z; Li, Y Q; Wang, XiaoGuang; Li, HaiBin; Sun, Zhe; Li, You-Quan
2005-01-01
By using the concept of negativity, we study entanglement in spin-one Heisenberg chains. Both the bilinear chain and the bilinear-biquadratic chain are considered. Due to the SU(2) symmetry, the negativity can be determined by two correlators, which greatly facilitate the study of entanglement properties. Analytical results of negativity are obtained in the bilinear model up to four spins and the two-spin bilinear-biquadratic model, and numerical results of negativity are presented. We determine the threshold temperature before which the thermal state is doomed to be entangled.
Entanglement in spin-1 Heisenberg XY chain
Institute of Scientific and Technical Information of China (English)
2008-01-01
We investigated the quantum entanglement in spin-1 Heisenberg XY chain for two-spin-qutrit and multi-particle systems. As a measure of the entanglement, the negativity of this state was analyzed as a function of the temperature and the magnetic field. We gave some numerical results and discussed them in detail. We found that the negativity increases monotonously with the coupling constants |J1| and |J2|, and it showed a symmetry with respect to the point of J1=0 and J2=0. In addition to the above features, there is evidence that the critical temperature is independent of the length of the chain.
Entanglement in spin-1 Heisenberg XY chain
Institute of Scientific and Technical Information of China (English)
QIN Meng; TAO YingJuan; HU MingLiang; TIAN DongPing
2008-01-01
We investigated the quantum entanglement in spin-1 Heisenberg XY chain for two-spin-qutrit and multi-particle systems. As a measure of the entanglement, the negativity of this state was analyzed as a function of the temperature and the magnetic field. We gave some numerical results and discussed them in detail. We found that the negativity increases monotonously with the coupling constants |J1|and |J2|, and it showed a symmetry with respect to the point of J1=0 and J2= 0. In addition to the above features, there is evidence that the critical temperature is independent of the length of the chain.
Quantum Correlations in Heisenberg XY Chain
Institute of Scientific and Technical Information of China (English)
ZHU Yin-Yan; ZHANG Yong
2013-01-01
Quantum correlations measured by quantum discord (QD),measurement-induced distance (MID),and geometric measure of quantum discord (GMQD) in two-qubit Heisenberg XY spin chain are investigated.The effects of DM interaction and anisotropic on the three correlations are considered.Characteristics of various correlation measures for the two-qubit states are compared.The increasing Dz increases QD,MID and GMQD monotonously while the increasing anisotropy both increases and decreases QD and GMQD.The three quantum correlations are always existent at very high temperature.MID is always larger than QD,but there is no definite ordering between QD and GMQD.
Magnetic properties of doped Heisenberg chains
Energy Technology Data Exchange (ETDEWEB)
Frahm, Holger; Slavnov, Nikita A
2000-06-05
The magnetic susceptibility of systems from a class of integrable models for doped spin-S Heisenberg chains is calculated in the limit of vanishing magnetic field. For small concentrations x{sub h} of the mobile spin-(S-1/2) charge carriers we find an explicit expression for the contribution of the gapless mode associated to the magnetic degrees of freedom of these holes to the susceptibility which exhibits a singularity for x{sub h}{yields}0 for sufficiently large S. We prove a sum rule for the contributions of the two gapless magnetic modes in the system to the susceptibility which holds for arbitrary hole concentration. This sum rule complements the one for the low temperature specific heat which has been obtained previously.
The spin-partitioned total position-spread tensor: An application to Heisenberg spin chains.
Fertitta, Edoardo; El Khatib, Muammar; Bendazzoli, Gian Luigi; Paulus, Beate; Evangelisti, Stefano; Leininger, Thierry
2015-12-28
The spin partition of the Total Position-Spread (TPS) tensor has been performed for one-dimensional Heisenberg chains with open boundary conditions. Both the cases of a ferromagnetic (high-spin) and an anti-ferromagnetic (low-spin) ground-state have been considered. In the case of a low-spin ground-state, the use of alternating magnetic couplings allowed to investigate the effect of spin-pairing. The behavior of the spin-partitioned TPS (SP-TPS) tensor as a function of the number of sites turned to be closely related to the presence of an energy gap between the ground-state and the first excited-state at the thermodynamic limit. Indeed, a gapped energy spectrum is associated to a linear growth of the SP-TPS tensor with the number of sites. On the other hand, in gapless situations, the spread presents a faster-than-linear growth, resulting in the divergence of its per-site value. Finally, for the case of a high-spin wave function, an analytical expression of the dependence of the SP-TPS on the number of sites n and the total spin-projection Sz has been derived.
The spin-partitioned total position-spread tensor: An application to Heisenberg spin chains
Energy Technology Data Exchange (ETDEWEB)
Fertitta, Edoardo; Paulus, Beate [Institut für Chemie und Biochemie, Freie Universität Berlin, Takustr. 3, 14195 Berlin (Germany); El Khatib, Muammar; Evangelisti, Stefano; Leininger, Thierry [Laboratoire de Chimie et Physique Quantiques–LCPQ/IRSAMC, Université de Toulouse (UPS) et CNRS (UMR-5626), 118 Route de Narbonne, Toulouse Cedex 31062 (France); Bendazzoli, Gian Luigi [Dipartimento di Chimica Industriale “Toso Montanari,” Università di Bologna, Viale Risorgimento 4, I–40136 Bologna (Italy)
2015-12-28
The spin partition of the Total Position-Spread (TPS) tensor has been performed for one-dimensional Heisenberg chains with open boundary conditions. Both the cases of a ferromagnetic (high-spin) and an anti-ferromagnetic (low-spin) ground-state have been considered. In the case of a low-spin ground-state, the use of alternating magnetic couplings allowed to investigate the effect of spin-pairing. The behavior of the spin-partitioned TPS (SP-TPS) tensor as a function of the number of sites turned to be closely related to the presence of an energy gap between the ground-state and the first excited-state at the thermodynamic limit. Indeed, a gapped energy spectrum is associated to a linear growth of the SP-TPS tensor with the number of sites. On the other hand, in gapless situations, the spread presents a faster-than-linear growth, resulting in the divergence of its per-site value. Finally, for the case of a high-spin wave function, an analytical expression of the dependence of the SP-TPS on the number of sites n and the total spin-projection S{sub z} has been derived.
Teleportation via thermally entangled states of a two-qubit Heisenberg XXZ chain
Institute of Scientific and Technical Information of China (English)
QIN Meng; TAO Ying-Juan; TIAN Dong-Ping
2008-01-01
We investigate quantum teleportation as a tool to study the thermally entangled state of a twoqubit Heisenberg XXZ chain.Our work is mainly to investigate the characteristics of a Heisenberg XXZ chain and get some analytical results of the fully entangled fraction.We also consider the entanglement teleportation via a two-qubit Heisenberg XXZ chain.
Phonon dynamics in a compressible classical Heisenberg chain
Fivez, Jan; Raedt, Hans De; Raedt, Bart De
1980-01-01
The dynamic properties of the compressible classical Heisenberg chain with bilinear coupling are investigated. The sound velocity is calculated exactly. The Fourier-transformed displacement-displacement correlation function is studied as a function of temperature, wave vector, and the model paramete
Spin Waves in a Classical Compressible Heisenberg Chain
Fivez, J.; Raedt, H. De
1980-01-01
The effect of the spin—lattice interaction on the spin dynamics of a classical Heisenberg chain is studied by means of a truncated continued fraction. At low temperature, the spin correlation length and the spin wave frequency show the same simple dependence on the coupling.
Entanglement of Two-Qubit Quantum Heisenberg XYZ Chain
Institute of Scientific and Technical Information of China (English)
惠小强; 郝三如; 陈文学; 岳瑞宏
2002-01-01
We derive the analytic expression of the concurrence in the quantum Heisenberg XY Z model and discuss the influence of parameters J, △ and Γ on the concurrence. By choosing different values of Γ and △, we obtain the XX, XY, XXX and XXZ chains. The concurrence decreases with increasing temperature. When entanglement. For the XXZ chain, when Γ→∞, the concurence will meet its maximum value Cmax= sinh(1/T)--cosh(1/T)@
Thermal quantum discord in the Heisenberg chain with impurity
Energy Technology Data Exchange (ETDEWEB)
Gong, Jia-Min, E-mail: jmgong@yeah.net; Hui, Zhan-Qiang
2014-07-01
We study thermal quantum discord (TQD) in the Heisenberg chain with spin site or magnetic impurity. The former one of which may induce inhomogeneous exchange interactions between the neighboring spins, while the latter one may model a spin chain with nonuniform magnetic field. In contrast to one's traditional understanding, we found that the spin impurity can be used to enhance the TQD greatly for all the bipartition schemes of the chain, while the magnetic impurity located on one spin can make the TQD between the other two spins approaching its maximum 1 for the antiferromagnetic chain.
Topological magnon bound-states in quantum Heisenberg chains
Qin, Xizhou; Ke, Yongguan; Zhang, Li; Lee, Chaohong
2016-01-01
It is still an outstanding challenge to characterize and understand the topological features of strongly correlated states such as bound-states in interacting multi-particle quantum systems. Recently, bound states of elementary spin waves (magnons) in quantum magnets have been experimentally observed in quantum Heisenberg chains comprising ultracold Bose atoms in optical lattices. Here, we explore an unprecedented topological state called topological magnon bound-state in the quantum Heisenberg chain under cotranslational symmetry. We find that the cotranslational symmetry allows us to formulate a direct topological invariant for the multi-particle quantum states, which can be used to characterize the topological features of multi-magnon excitations. We calculate energy spectra, density distributions, correlations and topological invariants of the two-magnon bound-states and show the existence of topological magnon bound-states. Our study not only opens a new prospect to pursue topological bound-states, but a...
Entanglement in Anisotropic Heisenberg XYZ Chain with Inhomogeneous Magnetic Field
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The thermal entanglement of a two-qubit anisotropic Heisenberg XYZ chain under an inhomogeneous magnetic field b is studied. It is shown that when inhomogeneity is increased to a certain value, the entanglement can exhibit a larger revival than that of less values of b. The property is both true for zero temperature and a finite temperature. The results also show that the entanglement and threshold temperature can be increased by increasing inhomogeneous external magnetic field.
Quantum Monte Carlo Study of Random Antiferromagnetic Heisenberg Chain
Todo, Synge; Kato, Kiyoshi; Takayama, Hajime
1998-01-01
Effects of randomness on the spin-1/2 and 1 antiferromagnetic Heisenberg chains are studied using the quantum Monte Carlo method with the continuous-time loop algorithm. We precisely calculated the uniform susceptibility, string order parameter, spatial and temporal correlation length, and the dynamical exponent, and obtained a phase diagram. The generalization of the continuous-time loop algorithm for the systems with higher-S spins is also presented.
Low-temperature transport in Heisenberg chains.
Alvarez, J V; Gros, Claudius
2002-02-18
A technique to determine accurately transport properties of integrable and nonintegrable quantum-spin chains at finite temperatures by quantum Monte Carlo is presented. The reduction of the Drude weight by interactions in the integrable gapless regime is evaluated. Evidence for the absence of Drude weight in the gapless regime of a nonintegrable system with longer-ranged interactions is presented. We estimate the effect of the nonintegrability on the transport properties and compare with recent experiments on one-dimensional quantum-spin chains.
Exact Haldane mapping for all S and super universality in spin chains
Pruisken, A.M.M.; Shankar, R.; Surendran, N.
2008-01-01
The low-energy dynamics of the anti-ferromagnetic Heisenberg spin S chain in the semiclassical limit S -> infinity is known to map onto the O(3) nonlinear alpha-model with a theta term in 1 + 1 dimension. Guided by the underlying dual symmetry of the spin chain, as well as by the recently establishe
Quantum spin transistor with a Heisenberg spin chain
Marchukov, O. V.; Volosniev, A. G.; Valiente, M.; Petrosyan, D.; Zinner, N. T.
2016-10-01
Spin chains are paradigmatic systems for the studies of quantum phases and phase transitions, and for quantum information applications, including quantum computation and short-distance quantum communication. Here we propose and analyse a scheme for conditional state transfer in a Heisenberg XXZ spin chain which realizes a quantum spin transistor. In our scheme, the absence or presence of a control spin excitation in the central gate part of the spin chain results in either perfect transfer of an arbitrary state of a target spin between the weakly coupled input and output ports, or its complete blockade at the input port. We also discuss a possible proof-of-concept realization of the corresponding spin chain with a one-dimensional ensemble of cold atoms with strong contact interactions. Our scheme is generally applicable to various implementations of tunable spin chains, and it paves the way for the realization of integrated quantum logic elements.
Quantum spin transistor with a Heisenberg spin chain
Marchukov, O. V.; Volosniev, A. G.; Valiente, M.; Petrosyan, D.; Zinner, N. T.
2016-01-01
Spin chains are paradigmatic systems for the studies of quantum phases and phase transitions, and for quantum information applications, including quantum computation and short-distance quantum communication. Here we propose and analyse a scheme for conditional state transfer in a Heisenberg XXZ spin chain which realizes a quantum spin transistor. In our scheme, the absence or presence of a control spin excitation in the central gate part of the spin chain results in either perfect transfer of an arbitrary state of a target spin between the weakly coupled input and output ports, or its complete blockade at the input port. We also discuss a possible proof-of-concept realization of the corresponding spin chain with a one-dimensional ensemble of cold atoms with strong contact interactions. Our scheme is generally applicable to various implementations of tunable spin chains, and it paves the way for the realization of integrated quantum logic elements. PMID:27721438
Quasiparticle interactions in frustrated Heisenberg chains
Vanderstraeten, Laurens; Haegeman, Jutho; Verstraete, Frank; Poilblanc, Didier
2016-06-01
Interactions between elementary excitations in quasi-one-dimensional antiferromagnets are of experimental relevance and their quantitative theoretical treatment has been a theoretical challenge for many years. Using matrix product states, one can explicitly determine the wave functions of the one- and two-particle excitations, and, consequently, the contributions to dynamical correlations. We apply this framework to the (nonintegrable) frustrated dimerized spin-1/2 chain, a model for generic spin-Peierls systems, where low-energy quasiparticle excitations are bound states of topological solitons. The spin structure factor involving two quasiparticle scattering states is obtained in the thermodynamic limit with full momentum and frequency resolution. This allows very subtle features in the two-particle spectral function to be revealed which, we argue, could be seen, e.g., in inelastic neutron scattering of spin-Peierls compounds under a change of the external pressure.
Macroscooic inequivalent entanglement witness in Heisenberg spin Chain
Institute of Scientific and Technical Information of China (English)
Zhang Ting; Chen Ping-Xing; Li Cheng-Zu
2009-01-01
Motivated by the wise idea of entanglement witness(EW),we present an inequivalent entanglement witness(IEEW)that can analogously classify certain eigenstates entangled in inequivalent ways under stochastic local operations and classical communication(SLOCC)in the Heisenberg spin chain.Since the IEEW is the absolute value of magnetization |M| that is a macroscopically measurable quantity,our conclusions provide a macroscopic method to detect incquivalent entanglement between microscopic spins,on the one hand,and clearly show that inequivalent entanglement can yield different macroscopic effects,on the other hand.
Q-operators for the open Heisenberg spin chain
Frassek, Rouven
2015-01-01
We construct Q-operators for the open spin-1/2 XXX Heisenberg spin chain with diagonal boundary matrices. The Q-operators are defined as traces over an infinite-dimensional auxiliary space involving novel types of reflection operators derived from the boundary Yang-Baxter equation. We argue that the Q-operators defined in this way are polynomials in the spectral parameter and show that they commute with transfer matrix. Finally, we prove that the Q-operators satisfy Baxter's TQ-equation.
Q-operators for the open Heisenberg spin chain
Directory of Open Access Journals (Sweden)
Rouven Frassek
2015-12-01
Full Text Available We construct Q-operators for the open spin-12 XXX Heisenberg spin chain with diagonal boundary matrices. The Q-operators are defined as traces over an infinite-dimensional auxiliary space involving novel types of reflection operators derived from the boundary Yang–Baxter equation. We argue that the Q-operators defined in this way are polynomials in the spectral parameter and show that they commute with transfer matrix. Finally, we prove that the Q-operators satisfy Baxter's TQ-equation and derive the explicit form of their eigenvalues in terms of the Bethe roots.
Q-operators for the open Heisenberg spin chain
Frassek, Rouven; Szécsényi, István M.
2015-12-01
We construct Q-operators for the open spin-1/2 XXX Heisenberg spin chain with diagonal boundary matrices. The Q-operators are defined as traces over an infinite-dimensional auxiliary space involving novel types of reflection operators derived from the boundary Yang-Baxter equation. We argue that the Q-operators defined in this way are polynomials in the spectral parameter and show that they commute with transfer matrix. Finally, we prove that the Q-operators satisfy Baxter's TQ-equation and derive the explicit form of their eigenvalues in terms of the Bethe roots.
Entanglement Transfer via XXZ Heisenberg chain with DM Interaction
Rafiee, Morteza; Mohammadi, Hamidreza; Mokhtari, Hossein
2010-01-01
The role of spin-orbit interaction, arises from the Dzyaloshinski-Moriya anisotropic antisymmetric interaction, on the entanglement transfer via an antiferromagnetic XXZ Heisenberg chain is investigated. From symmetrical point of view, the XXZ Hamiltonian with Dzyaloshinski-Moriya interaction can be replaced by a modified XXZ Hamiltonian which is defined by a new exchange coupling constant and rotated Pauli operators. The modified coupling constant and the angle of rotations are depend on the strength of Dzyaloshinski-Moriya interaction. In this paper we study the dynamical behavior of the entanglement propagation through a system which is consist of a pair of maximally entangled spins coupled to one end of the chain. The calculations are performed for the ground state and the thermal state of the chain, separately. In both cases the presence of this anisotropic interaction make our channel more efficient, such that the speed of transmission and the amount of the entanglement are improved as this interaction ...
Spectral Duality Between Heisenberg Chain and Gaudin Model
Mironov, A; Runov, B; Zenkevich, Y; Zotov, A
2012-01-01
In our recent paper we described relationships between integrable systems inspired by the AGT conjecture. On the gauge theory side an integrable spin chain naturally emerges while on the conformal field theory side one obtains some special reduced Gaudin model. Two types of integrable systems were shown to be related by the spectral duality. In this paper we extend the spectral duality to the case of higher spin chains. It is proved that the N-site GL(k) Heisenberg chain is dual to the special reduced k+2-points gl(N) Gaudin model. Moreover, we construct an explicit Poisson map between the models at the classical level by performing the Dirac reduction procedure and applying the AHH duality transformation.
Quantum correlations and coherence in spin-1 Heisenberg chains
Malvezzi, A. L.; Karpat, G.; ćakmak, B.; Fanchini, F. F.; Debarba, T.; Vianna, R. O.
2016-05-01
We explore quantum and classical correlations along with coherence in the ground states of spin-1 Heisenberg chains, namely the one-dimensional XXZ model and the one-dimensional bilinear biquadratic model, with the techniques of density matrix renormalization group theory. Exploiting the tools of quantum information theory, that is, by studying quantum discord, quantum mutual information, and three recently introduced coherence measures in the reduced density matrix of two nearest neighbor spins in the bulk, we investigate the quantum phase transitions and special symmetry points in these models. We point out the relative strengths and weaknesses of correlation and coherence measures as figures of merit to witness the quantum phase transitions and symmetry points in the considered spin-1 Heisenberg chains. In particular, we demonstrate that, as none of the studied measures can detect the infinite-order Kosterlitz-Thouless transition in the XXZ model, they appear to be able to signal the existence of the same type of transition in the biliear biquadratic model. However, we argue that what is actually detected by the measures here is the SU(3) symmetry point of the model rather than the infinite-order quantum phase transition. Moreover, we show in the XXZ model that examining even single site coherence can be sufficient to spotlight the second-order phase transition and the SU(2) symmetry point.
Local spin relaxation within the random Heisenberg chain.
Herbrych, J; Kokalj, J; Prelovšek, P
2013-10-04
Finite-temperature local dynamical spin correlations S(nn)(ω) are studied numerically within the random spin-1/2 antiferromagnetic Heisenberg chain. The aim is to explain measured NMR spin-lattice relaxation times in BaCu(2)(Si(0.5)Ge(0.5))(2)O(7), which is the realization of a random spin chain. In agreement with experiments we find that the distribution of relaxation times within the model shows a very large span similar to the stretched-exponential form. The distribution is strongly reduced with increasing T, but stays finite also in the high-T limit. Anomalous dynamical correlations can be associated with the random singlet concept but not directly with static quantities. Our results also reveal the crucial role of the spin anisotropy (interaction), since the behavior is in contrast with the ones for the XX model, where we do not find any significant T dependence of the distribution.
Continuous and Discrete (Classical Heisenberg Spin Chain Revised
Directory of Open Access Journals (Sweden)
Orlando Ragnisco
2007-02-01
Full Text Available Most of the work done in the past on the integrability structure of the Classical Heisenberg Spin Chain (CHSC has been devoted to studying the su(2 case, both at the continuous and at the discrete level. In this paper we address the problem of constructing integrable generalized ''Spin Chains'' models, where the relevant field variable is represented by a N × N matrix whose eigenvalues are the Nth roots of unity. To the best of our knowledge, such an extension has never been systematically pursued. In this paper, at first we obtain the continuous N × N generalization of the CHSC through the reduction technique for Poisson-Nijenhuis manifolds, and exhibit some explicit, and hopefully interesting, examples for 3 × 3 and 4 × 4 matrices; then, we discuss the much more difficult discrete case, where a few partial new results are derived and a conjecture is made for the general case.
Marques, Adílio Jorge; Departamento de Ciências Exatas, Biológicas e da Terra, Universidade Federal Fluminense
2015-01-01
Resenha do livro HeisenbergJosé Maria Filardo Bassalo e Francisco CarusoEditora Livraria da Física, São Paulo, 2014, 1a edição, 111 p.ISBN: 9788578612221http://dx.doi.org/10.5007/2175-7941.2015v32n1p291 Review of the book HeisenbergJosé Maria Filardo Bassalo e Francisco CarusoEditora Livraria da Física, São Paulo, 2014, 1a edição, 111 p.ISBN: 9788578612221http://dx.doi.org/10.5007/2175-7941.2015v32n1p291
Entanglement in an anisotropic spin-1 Heisenberg chain
Institute of Scientific and Technical Information of China (English)
Zhu Yan; Zhu Shi-Qun; Hao Xiang
2007-01-01
The entanglement in an anisotropic spin-1 Heisenberg chain with a uniform magnetic field is investigated. The ground-state entanglement will undergo two different kinds of transitions when the anisotropy △ and the amplitude of the magnetic field B are varied. The thermal entanglement of the nearest neighbour always declines when B increases no matter what the value of the anisotropy is. It is very interesting to note that the entanglement of the next-nearest neighbour can increase to a maximum at a certain magnetic field. Regardless of the boundary condition, the nearest-neighbour entanglement always decreases and approaches to a constant value when the size of the system is very large. The constant value of open boundary condition is much larger than that of periodic boundary condition.
Spin supersolid in an anisotropic spin-one Heisenberg chain.
Sengupta, P; Batista, C D
2007-11-23
We consider an S=1 Heisenberg chain with strong exchange (Delta=J(z)/J(perpendicular)) and single-ion uniaxial anisotropy (D) in a magnetic field (B) along the symmetry axis. The low-energy spectrum is described by an effective S=1/2 XXZ model that acts on two different low-energy sectors for a finite range of fields. The vacuum of each sector exhibits Ising-like antiferromagnetic ordering coexisting with the finite spin stiffness obtained from the exact solution of the XXZ model. In this way, we demonstrate the existence of a spin supersolid phase. We also compute the full Delta-B quantum phase diagram using a quantum Monte Carlo method.
Distribution of NMR relaxations in a random Heisenberg chain.
Shiroka, T; Casola, F; Glazkov, V; Zheludev, A; Prša, K; Ott, H-R; Mesot, J
2011-04-01
NMR measurements of the (29)Si spin-lattice relaxation time T(1) were used to probe the spin-1/2 random Heisenberg chain compound BaCu(2)(Si(1-x)Ge(x))(2)O(7). Remarkable differences between the pure (x=0) and the fully random (x=0.5) cases are observed, indicating that randomness generates a distribution of local magnetic relaxations. This distribution, which is reflected in a stretched exponential NMR relaxation, exhibits a progressive broadening with decreasing temperature, caused by a growing inequivalence of magnetic sites. Compelling independent evidence for the influence of randomness is also obtained from magnetization data and Monte Carlo calculations. These results suggest the formation of random-singlet states in this class of materials, as previously predicted by theory.
Variational Monte Carlo investigation of SU (N ) Heisenberg chains
Dufour, Jérôme; Nataf, Pierre; Mila, Frédéric
2015-05-01
Motivated by recent experimental progress in the context of ultracold multicolor fermionic atoms in optical lattices, we have investigated the properties of the SU (N) Heisenberg chain with totally antisymmetric irreducible representations, the effective model of Mott phases with m Gutzwiller projected fermionic wave functions, we have been able to verify these predictions for a representative number of cases with N ≤10 and m ≤N /2 , and we have shown that the opening of a gap is associated to a spontaneous dimerization or trimerization depending on the value of m and N . We have also investigated the marginal cases where Abelian bosonization did not lead to any prediction. In these cases, variational Monte Carlo predicts that the ground state is critical with exponents consistent with conformal field theory.
Excited state correlations of the finite Heisenberg chain
Pozsgay, Balázs
2017-02-01
We consider short range correlations in excited states of the finite XXZ and XXX Heisenberg spin chains. We conjecture that the known results for the factorized ground state correlations can be applied to the excited states too, if the so-called physical part of the construction is changed appropriately. For the ground state we derive simple algebraic expressions for the physical part; the formulas only use the ground state Bethe roots as an input. We conjecture that the same formulas can be applied to the excited states as well, if the exact Bethe roots of the excited states are used instead. In the XXZ chain the results are expected to be valid for all states (except certain singular cases where regularization is needed), whereas in the XXX case they only apply to singlet states or group invariant operators. Our conjectures are tested against numerical data from exact diagonalization and coordinate Bethe Ansatz calculations, and perfect agreement is found in all cases. In the XXX case we also derive a new result for the nearest-neighbour correlator , which is valid for non-singlet states as well. Our results build a bridge between the known theory of factorized correlations, and the recently conjectured TBA-like description for the building blocks of the construction.
Nonreciprocal spin wave elementary excitation in dislocated dimerized Heisenberg chains.
Liu, Wanguo; Shen, Yang; Fang, Guisheng; Jin, Chongjun
2016-05-18
A mechanism for realizing nonreciprocal elementary excitation of spin wave (SW) is proposed. We study a reference model which describes a magnonic crystal (MC) formed by two Heisenberg chains with a lateral displacement (dislocation) and a longitudinal spacer, and derive a criterion to judge whether the elementary excitation spectra are reciprocal in this ferromagnetic lattice. An analytical method based on the spin precession equation is used to solve the elementary excitation spectra. The solution is related to a key factor, the spatio-temporal structure factor [Formula: see text], which can be directly calculated through the structural parameters. When it keeps invariant under the reversions of the external magnetic field [Formula: see text] and the dislocation [Formula: see text], or one of them, the spectra are reciprocal. Otherwise, the SW possesses nonreciprocal spectra with direction-dependent band edges and exhibits a directional magnetoresistance effect. This criterion can be regarded as a necessary and sufficient condition for the (non)reciprocity in the spin lattice. Besides, this novel lattice provides a prototype for spin diodes and spin logic gates.
Spin diffusion in anisotropic Heisenberg chains: S{>=}1/2
Energy Technology Data Exchange (ETDEWEB)
Huber, D.L., E-mail: huber@src.wisc.edu [Physics Department, University of Wisconsin-Madison, 1150 University Avenue, Madison WI 53706 (United States)
2012-11-01
In this paper, we investigate spin diffusion in Heisenberg chains with uniaxial nearest-neighbor interactions. The approach followed is based on an analysis of the infinite-temperature longitudinal spin density and spin current correlation functions. For S=1/2, exact results are presented for the time-dependent correlation functions in the XY limit. Away from this limit, the second and fourth moments of the Fourier transform of the spin density correlation function provide information about spin dynamics for arbitrary values of the spin. The moments are used in an assessment of the accuracy of the Gaussian approximation for the spin diffusion constant for S=1/2. The general behavior of the Gaussian approximation when S>1/2 is discussed, and numerical results for the spin diffusion constant are presented for S=1/2, 1, 3/2, 2 and in the classical limit. A moment-based criterion for the boundary in reciprocal space between diffusive and non-diffusive dynamics that applies to arbitrary values of the spin is presented.
New Universality Class in the S=1/2 Fibonacci Heisenberg Chains
Hida, Kazuo
2004-01-01
Low energy properties of the S=1/2 antiferromagnetic Heisenberg chains with Fibonacci exchange modulation are studied using the real space renormalization group method for strong exchange modulation. It is found that the ground state of this model belongs to a new universality class with logarithmically divergent dynamical exponent which is neither like Fibonacci XY chains nor like XY chains with relevant aperiodicity.
Entropy Squeezing in the Quantum Heisenberg XY Spin Chains
Institute of Scientific and Technical Information of China (English)
CHANG Ping; SHAO Bin; ZOU Jian
2009-01-01
The time evolution of entropy squeezing for the two-qubit XYZ Heisenberg model in an external uniform magnetic field is investigated in the language of quantum information.The effect of different parameters such as magnetic field and anisotropy parameter on the properties of entropy squeezing and variance squeezing are discussed.It is shown that magnetic field and anisotropy parameter can enhance the entropy squeezing.
Quasilocal Conserved Operators in the Isotropic Heisenberg Spin-1/2 Chain.
Ilievski, Enej; Medenjak, Marko; Prosen, Tomaž
2015-09-18
Composing higher auxiliary-spin transfer matrices and their derivatives, we construct a family of quasilocal conserved operators of isotropic Heisenberg spin-1/2 chain and rigorously establish their linear independence from the well-known set of local conserved charges.
Quasilocal Conserved Operators in the Isotropic Heisenberg Spin-1/2 Chain
Ilievski, E.; Medenjak, M.; Prosen, T.
2015-01-01
Composing higher auxiliary-spin transfer matrices and their derivatives, we construct a family of quasilocal conserved operators of isotropic Heisenberg spin-1/2 chain and rigorously establish their linear independence from the well-known set of local conserved charges.
The magnetic properties of the spin-1 Heisenberg antiferromagnetic chain with single-ion anisotropy
Energy Technology Data Exchange (ETDEWEB)
Hu, Gangsan; Zhu, Rengui, E-mail: rgzhu@mail.ahnu.edu.cn
2015-02-15
The magnetic properties of the spin-1 Heisenberg antiferromagnetic chain with exchange anisotropy and single-ion anisotropy are studied by the double-time Green's function method. The determinative equations for the critical temperature, the magnetization, and the zero-field susceptibility are derived analytically. The effects of the anisotropies on the magnetic properties are presented.
Intrinsic localized modes of a classical discrete anisotropic Heisenberg ferromagnetic spin chain
Energy Technology Data Exchange (ETDEWEB)
Lakshmanan, M., E-mail: lakshman@cnld.bdu.ac.in [Centre for Nonlinear Dynamics, Department of Physics, Bharathidasan University, Tiruchirapalli 620 024 (India); Subash, B. [Centre for Nonlinear Dynamics, Department of Physics, Bharathidasan University, Tiruchirapalli 620 024 (India); Saxena, Avadh [Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545 (United States)
2014-03-01
We report several exact intrinsic localized mode solutions of the classical spin evolution equation of a one-dimensional anisotropic Heisenberg ferromagnetic spin chain in terms of Jacobian elliptic functions. These include one, two and three spin excitations. All these solutions have smooth anticontinuum limits. Their linear stability and semiclassical quantization are also discussed briefly.
Verkholyak, Taras; Strečka, Jozef
2016-10-01
The spin-1/2 Heisenberg orthogonal-dimer chain is considered within the perturbative strong-coupling approach, which is developed from the exactly solved spin-1/2 Ising-Heisenberg orthogonal-dimer chain with the Heisenberg intradimer and the Ising interdimer couplings. Although the spin-1/2 Ising-Heisenberg orthogonal-dimer chain exhibits just intermediate plateaus at zero, one-quarter, and one-half of the saturation magnetization, the perturbative treatment up to second order stemming from this exactly solvable model additionally corroborates the fractional one-third plateau as well as the gapless Luttinger spin-liquid phase. It is evidenced that the approximate results obtained from the strong-coupling approach are in an excellent agreement with the state-of-the-art numerical data obtained for the spin-1/2 Heisenberg orthogonal-dimer chain within the exact diagonalization and density-matrix renormalization group method. The nature of individual quantum ground states is comprehensively studied within the developed perturbation theory.
Topological basis realization for BMW algebra and Heisenberg XXZ spin chain model
Liu, Bo; Xue, Kang; Wang, Gangcheng; Liu, Ying; Sun, Chunfang
2015-04-01
In this paper, we study three-dimensional (3D) reduced Birman-Murakami-Wenzl (BMW) algebra based on topological basis theory. Several examples of BMW algebra representations are reviewed. We also discuss a special solution of BMW algebra, which can be used to construct Heisenberg XXZ model. The theory of topological basis provides a useful method to solve quantum spin chain models. It is also shown that the ground state of XXZ spin chain is superposition state of topological basis.
Low Energy Properties of the Random Spin-1/2 Ferromagnetic-Antiferromagnetic Heisenberg Chain
Hida, Kazuo
1996-01-01
The low energy properties of the spin-1/2 random Heisenberg chain with ferromagnetic and antiferromagnetic interactions are studied by means of the density matrix renormalization group (DMRG) and real space renormalization group (RSRG) method for finite chains. The results of the two methods are consistent with each other. The deviation of the gap distribution from that of the random singlet phase and the formation of the large-spin state is observed even for relatively small systems. For a s...
Antiferromagnetic Heisenberg Spin Chain of a Few Cold Atoms in a One-Dimensional Trap.
Murmann, S; Deuretzbacher, F; Zürn, G; Bjerlin, J; Reimann, S M; Santos, L; Lompe, T; Jochim, S
2015-11-20
We report on the deterministic preparation of antiferromagnetic Heisenberg spin chains consisting of up to four fermionic atoms in a one-dimensional trap. These chains are stabilized by strong repulsive interactions between the two spin components without the need for an external periodic potential. We independently characterize the spin configuration of the chains by measuring the spin orientation of the outermost particle in the trap and by projecting the spatial wave function of one spin component on single-particle trap levels. Our results are in good agreement with a spin-chain model for fermionized particles and with numerically exact diagonalizations of the full few-fermion system.
Gomez, Alejandro De La Rosa; Regelskis, Vidas
2016-01-01
We present a general method of folding an integrable spin chain, defined on a line, to obtain an integrable open spin chain, defined on a half-line. We illustrate our method through two fundamental models with sl(2) Lie algebra symmetry: the Heisenberg XXX and the Inozemtsev hyperbolic spin chains. We obtain new long-range boundary Hamiltonians and demonstrate that they exhibit Yangian symmetries, thus ensuring integrability of the models we obtain. The method presented provides a "bottom-up" approach for constructing integrable boundaries and can be applied to any spin chain model.
An Effective Heisenberg Spin Chain in a Fiber-Cavity System
Institute of Scientific and Technical Information of China (English)
钟志荣; 张斌; 林秀; 苏万钧
2011-01-01
We propose a scheme to realize the Heisenberg spin chain in a one-dimensional array of cavities connected by-optical fibers. The proposed scheme is based on the off-resonant Raman transitions between two ground states of atoms, and is induced by the cavity modes and external Gelds. Under the interactions between the nearest neighbors (NNs) and the next NNs, the result shows that the atoms, via the exchange of virtual photons, can be effectively equal to a spin-1/2 Heisenberg model under certain conditions. The parameters of the effective Hamiltonian can be controlled by tuning the laser fields.%We propose a scheme to realize the Heisenberg spin chain in a one-dimensional array of cavities connected by optical fibers.The proposed scheme is based on the off-resonant Raman transitions between two ground states of atoms,and is induced by the cavity modes and external fields.Under the interactions between the nearest neighbors(NNs)and the next NNs,the result shows that the atoms,via the exchange of virtual photons,can be effectively equal to a spin-1/2 Heisenberg model under certain conditions.The parameters of the effective Hamiltonian can be controlled by tuning the laser fields.
Event-chain algorithm for the Heisenberg model: Evidence for z≃1 dynamic scaling.
Nishikawa, Yoshihiko; Michel, Manon; Krauth, Werner; Hukushima, Koji
2015-12-01
We apply the event-chain Monte Carlo algorithm to the three-dimensional ferromagnetic Heisenberg model. The algorithm is rejection-free and also realizes an irreversible Markov chain that satisfies global balance. The autocorrelation functions of the magnetic susceptibility and the energy indicate a dynamical critical exponent z≈1 at the critical temperature, while that of the magnetization does not measure the performance of the algorithm. We show that the event-chain Monte Carlo algorithm substantially reduces the dynamical critical exponent from the conventional value of z≃2.
Frustrated diamond-chain quantum XXZ Heisenberg antiferromagnet in a magnetic field
Energy Technology Data Exchange (ETDEWEB)
Richter, Johannes, E-mail: Johannes.Richter@Physik.Uni-Magdeburg.DE [Institut für theoretische Physik, Otto-von-Guericke-Universität Magdeburg, P.O. Box 4120, D-39016 Magdeburg (Germany); Krupnitska, Olesia [Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, 1 Svientsitskii Street, L' viv-11, 79011 (Ukraine); Krokhmalskii, Taras [Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, 1 Svientsitskii Street, L' viv-11, 79011 (Ukraine); Department for Theoretical Physics, Ivan Franko National University of L' viv, 12 Drahomanov Street, L' viv-5, 79005 (Ukraine); Derzhko, Oleg [Institut für theoretische Physik, Otto-von-Guericke-Universität Magdeburg, P.O. Box 4120, D-39016 Magdeburg (Germany); Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, 1 Svientsitskii Street, L' viv-11, 79011 (Ukraine); Department for Theoretical Physics, Ivan Franko National University of L' viv, 12 Drahomanov Street, L' viv-5, 79005 (Ukraine); Abdus Salam International Centre for Theoretical Physics, Strada Costiera 11, I-34151 Trieste (Italy)
2015-04-01
We consider the antiferromagnetic spin-1/2 XXZ Heisenberg model on a frustrated diamond-chain lattice in a z- or x-aligned external magnetic field. We use the strong-coupling approach to elaborate an effective description in the low-temperature strong-field regime. The obtained effective models are spin-1/2 XY chains which are exactly solvable through the Jordan–Wigner fermionization. We perform exact-diagonalization studies of the magnetization curves to test the quality of the effective description. The results may have relevance for the description of the azurite spin-chain compound.
A quaternionic map for the steady states of the Heisenberg spin-chain
Energy Technology Data Exchange (ETDEWEB)
Mehta, Mitaxi P., E-mail: mitaxi.mehta@ahduni.edu.in [IICT, Ahmedabad University, Opp. IIM, Navrangpura, Ahmedabad (India); Dutta, Souvik; Tiwari, Shubhanshu [BITS-Pilani, K.K. Birla Goa campus, Goa (India)
2014-01-17
We show that the steady states of the classical Heisenberg XXX spin-chain in an external magnetic field can be found by iterations of a quaternionic map. A restricted model, e.g., the xy spin-chain is known to have spatially chaotic steady states and the phase space occupied by these chaotic states is known to go through discrete changes as the field strength is varied. The same phenomenon is studied for the xxx spin-chain. It is seen that in this model the phase space volume varies smoothly with the external field.
New Universality Class in Spin-One-Half Fibonacci Heisenberg Chains
Hida, Kazuo
2004-07-01
Low energy properties of the S=1/2 antiferromagnetic Heisenberg chains with Fibonacci exchange modulation are studied using the real space renormalization group method for strong exchange modulation. Using the analytical solution of the recursion equation, the true asymptotic behavoir is revealed, which was veiled by the finite size effect in the previous numerical works. It is found that the ground state of this model belongs to a new universality class with a logarithmically divergent dynamical exponent which is neither like Fibonacci XY chains nor like XY chains with relevant aperiodicity.
Event-chain algorithm for the Heisenberg model: Evidence for z ≃1 dynamic scaling
Nishikawa, Yoshihiko; Michel, Manon; Krauth, Werner; Hukushima, Koji
2015-12-01
We apply the event-chain Monte Carlo algorithm to the three-dimensional ferromagnetic Heisenberg model. The algorithm is rejection-free and also realizes an irreversible Markov chain that satisfies global balance. The autocorrelation functions of the magnetic susceptibility and the energy indicate a dynamical critical exponent z ≈1 at the critical temperature, while that of the magnetization does not measure the performance of the algorithm. We show that the event-chain Monte Carlo algorithm substantially reduces the dynamical critical exponent from the conventional value of z ≃2 .
Exactly solved mixed spin-(1,1/2) Ising-Heisenberg distorted diamond chain
Lisnyi, Bohdan; Strečka, Jozef
2016-11-01
The mixed spin-(1,1/2) Ising-Heisenberg model on a distorted diamond chain with the spin-1 nodal atoms and the spin-1/2 interstitial atoms is exactly solved by the transfer-matrix method. An influence of the geometric spin frustration and the parallelogram distortion on the ground state, magnetization, susceptibility and specific heat of the mixed-spin Ising-Heisenberg distorted diamond chain are investigated in detail. It is demonstrated that the zero-temperature magnetization curve may involve intermediate plateaus just at zero and one-half of the saturation magnetization. The temperature dependence of the specific heat may have up to three distinct peaks at zero magnetic field and up to four distinct peaks at a non-zero magnetic field. The origin of multipeak thermal behavior of the specific heat is comprehensively studied.
Qi, F; Ma, Q Y; Qi, A Y; Xu, P; Zhu, S N; Zheng, W H
2016-01-01
Next-nearest-neighbor Heisenberg chain plays important roles in solid state physics, such as predicting exotic electric properties of two-dimensional materials or magnetic properties of organic compounds. Direct experimental studies of the many-body electron systems or spin systems associating to these materials are challenging tasks, while optical simulation provides an effective and economical way for immediate observation. Comparing with bulk optics, integrated optics are more of fascinating for steady, large scale and long-time evolution simulations. Photonic crystal is an artificial microstructure material with multiple methods to tune the propagation properties, which are essential for various simulation tasks. Here we report for the first time an experimental simulation of next-nearest-neighbor Heisenberg chain with an integrated optical chip of photonic crystal waveguide array. The use of photonic crystal enhances evanescent field thus allows coupling between next-nearest-neighbor waveguides in such a...
Algebraic Bethe ansatz for Q-operators: The Heisenberg spin chain
Frassek, Rouven
2015-01-01
We diagonalize Q-operators for rational homogeneous sl(2)-invariant Heisenberg spin chains using the algebraic Bethe ansatz. After deriving the fundamental commutation relations relevant for this case from the Yang-Baxter equation we demonstrate that the Q-operators act diagonally on the Bethe vectors if the Bethe equations are satisfied. In this way we provide a direct proof that the eigenvalues of the Q-operators studied here are given by Baxter's Q-functions.
Impurity in Pairwise Entanglement of Heisenberg ⅩⅩ Open Chain
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
We calculate the concurrence of all pairwise entanglement of Heisenberg ⅩⅩ open chain with single system impurity in three-qubit and four-qubit cases, and find that the impurity parameter Ji has great effect on pairwise entanglement. Choosing the proper parameter Ji, we can obtain the maximal pairwise entanglement of the nearest qubits and make the non-nearest qubits entangle.
Intrinsic Decoherence on Two-Qubit Heisenberg ⅩⅩ Chain
Institute of Scientific and Technical Information of China (English)
HE Zheng-Hong; XIONG Zu-Hong; HU Dong-Mei
2007-01-01
Quantum teleportation is investigated by using the entangled states of two-qubit Heisenberg ⅩⅩ chain in an external uniform magnetic field as resources in the model of Milburn's intrinsic decoherence. Though intrinsic decoherence on quantum entanglement and quantum teleportation exerts different effects in different initial systems,proper magnetic fields and probabilities of different eigenstates in the initial states can weaken the effects.
An Approach to Loop Quantum Cosmology Through Integrable Discrete Heisenberg Spin Chains
Dantas, Christine C
2012-01-01
The quantum evolution equation of Loop Quantum Cosmology (LQC) -- the quantum Hamiltonian constraint -- is a difference equation. We relate the LQC constraint equation in vacuum Bianchi I separable (locally rotationally symmetric) models with an integrable differential-difference nonlinear Schr\\"odinger type equation, which in turn is known to be associated with integrable, discrete Heisenberg spin chain models in condensed matter physics. We illustrate the similarity between both systems with a simple constraint in the linear regime.
Bipartite entanglement in a two-qubit Heisenberg XXZ chain under an inhomogeneous magnetic field
Institute of Scientific and Technical Information of China (English)
QIN Meng; TIAN Dong-Ping
2009-01-01
This paper investigates the bipartite entanglement of a two-qubit Heisenberg XXZ chain under an inhomogeneous magnetic field. By the concept of negativity, we find that the inhomogeneity of the magnetic field may induce entanglement and the critical magnetic field is independent of Jz. We also find that the entanglement is symmetric with respect to a zero magnetic field. The anisotropy parameter Jz may enhance the entanglement.
Analytical and numerical studies of disordered spin-1 Heisenberg chains with aperiodic couplings
Grande, H. L. Casa; Laflorencie, N.; Alet, F.; Vieira, A. P.
2013-01-01
We investigate the low-temperature properties of the one-dimensional spin-1 Heisenberg model with geometric fluctuations induced by aperiodic but deterministic coupling distributions, involving two parameters. We focus on two aperiodic sequences, the Fibonacci sequence and the 6-3 sequence. Our goal is to understand how these geometric fluctuations modify the physics of the (gapped) Haldane phase, which corresponds to the ground state of the uniform spin-1 chain. We make use of different adap...
Thermal entanglement of the Ising Heisenberg diamond chain with Dzyaloshinskii Moriya interaction
Institute of Scientific and Technical Information of China (English)
谯洁; 周斌
2015-01-01
We investigate the thermal entanglement in a spin-1/2 Ising–Heisenberg diamond chain, in which the vertical Heisen-berg spin dimers alternate with single Ising spins. Due to the fact that the Dzyaloshinskii–Moriya (DM) interaction con-tributes to unusual and interesting magnetic properties in actual materials, and moreover it plays a significant role in the degree of the entanglement of the Heisenberg quantum spin systems, we focus on the effects of different DM interactions, including Dz and Dx , on the thermal entanglement of the Heisenberg spin dimer. The concurrence, as a measure of spin dimer entanglement, is calculated for different values of exchange interactions, DM interaction, external magnetic field, and temperature. It is found that the critical temperature and the critical magnetic field corresponding to the vanishing of entanglement increase with DM interaction, and the entanglement revival region gets larger by increasing DM interac-tion, thus DM interaction favors the formation of the thermal entanglement. It is observed that different DM interaction parameters (Dz and Dx) have remarkably different infl uences on the entanglement. Different from the case Dz, there is the non-monotonic variation of the concurrence with temperature in the case Dx , and additionally the DM interaction Dx can induce the entanglement near zero temperature in the case that the antiferromagnetic Ising-type interaction constant is larger than the antiferromagnetic Heisenberg interaction constant. It is also shown that for the same value of DM interaction the critical magnetic field of the case Dx is larger than that of the case Dz.
Energy Technology Data Exchange (ETDEWEB)
Cui, L.; Wang, F. [Suqian College, Fundamental Department, Suqian 223800 (China); Zhang, S.J. [Hubei University of Automotive Technology, Shiyan 442002 (China); Hu, Y.J., E-mail: eric8222@126.com [Hubei University of Automotive Technology, Shiyan 442002 (China)
2014-10-15
Using exact numerical diagonalization and density-matrix renormalization group method, we study the effect of magnetic frustrations due to next-nearest-neighbor bonds in a structure of periodically doping spins beside every spin side of the same sublattice of the 1D HAF linear chain, which is popularly known as Quasi-One-Dimensional Heisenberg Antiferromagnetic chain. As a result of the frustrations, the quantum disordered phase (gapped) also appears in the quantum case, except that the ferrimagnetic state in the non-frustrations case and the caned phase appeared in the classical case. For quantum disordered phase, tetramer–dimmer state is predominant and the spin gap is opened.
Energy Technology Data Exchange (ETDEWEB)
Rojas, Onofre, E-mail: ors@dex.ufla.br [Departamento de Ciencias Exatas, Universidade Federal de Lavras, 37200-000, Lavras-MG (Brazil); Strečka, Jozef [Department of Theoretical Physics and Astrophysics, Faculty of Science, P.J. Šafárik University, Park Angelinum 9, 040 01 Košice (Slovakia); Lyra, Marcelo L. [Instituto de Física, Universidade Federal de Alagoas, 57072-970, Maceio-AL (Brazil)
2013-05-03
The spin-1/2 Ising–Heisenberg tetrahedral chain is exactly solved using its local gauge symmetry (the total spin of the Heisenberg bonds is locally conserved) and the transfer-matrix approach. Exact results derived for spin–spin correlation functions are employed to obtain the frustration temperature. In addition, we have exactly calculated a concurrence quantifying thermal entanglement. It is shown that the frustration and threshold temperature coincide at sufficiently low temperatures, while they exhibit a very different behavior in the high-temperature region when tending towards completely different asymptotic limits. The threshold temperature additionally shows a notable reentrant behavior when it extends over a narrow temperature region above the classical ground state without any quantum correlations. -- Highlights: ► Using local gauge symmetry we solved the spin-1/2 Ising–Heisenberg tetrahedral chain. ► The frustration temperature was calculated using the correlation functions. ► Thermal entanglement, concurrence and threshold temperature were analyzed. ► The zero-field specific heat was exactly calculated and discussed.
Even-Odd Effects of Heisenberg Chains on Long-range Interaction and Entanglement
Oh, Sangchul; Hu, Xuedong
2010-01-01
A strongly coupled Heisenberg chain provides an important channel for quantum communication through its many-body ground state. Yet, the nature of the effective interactions and the ability to mediate long-range entanglement differs significantly for chains of opposite parity. Here, we contrast the characters of even and odd-size chains when they are coupled to external qubits. Additional parity effects emerge in both cases, depending on the positions of the attached qubits. Some striking results include (i) the emergence of maximal entanglement and (ii) Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions for qubits attached to an even chain, and (iii) the ability of chains of either parity to mediate qubit entanglement that is undiminished by distance.
Antiferromagnetic sawtooth chain with Heisenberg and Ising bonds
Directory of Open Access Journals (Sweden)
V. Ohanyan
2009-01-01
Full Text Available The sawtooth chain with pairs of S=1/2 spins interacting with XXZ-interactions placed on each second tooth is considered. All other interaction bonds are taken to be of Ising type. Exact statistical mechanical solution of the model within the direct transfer-matrix technique is obtained. The solution allows one to obtain exact analytic expressions for all thermodynamic functions of the model. Ground state properties are also investigated, the corresponding ground state phase diagram is presented.
Exotic Ground State Phases of S=1/2 Heisenberg Δ-Chain with Ferromagnetic Main Chain
Hida, Kazuo
2008-04-01
The ground state phase diagram of the spin-1/2 Heisenberg frustrated Δ-chain with a ferromagnetic main chain is investigated. In addition to the ferromagnetic phase, various nonmagnetic ground states are found. If the ferromagnetic coupling between apical spins and the main chain is strong, this model is approximated by a spin-1 bilinear-biquadratic chain and the spin quadrupolar phase with spin-2 gapless excitation is realized in addition to the Haldane and ferromagnetic phases. In the regime where the coupling between the apical spins and the main chain is weak, the numerical results which suggest the possibility of a series of phase transitions among different nonmagnetic phases are obtained. Physical pictures of these phases are discussed based on the numerical results.
Ground-state energies of the nonlinear sigma model and the Heisenberg spin chains
Zhang, Shoucheng; Schulz, H. J.; Ziman, Timothy
1989-01-01
A theorem on the O(3) nonlinear sigma model with the topological theta term is proved, which states that the ground-state energy at theta = pi is always higher than the ground-state energy at theta = 0, for the same value of the coupling constant g. Provided that the nonlinear sigma model gives the correct description for the Heisenberg spin chains in the large-s limit, this theorem makes a definite prediction relating the ground-state energies of the half-integer and the integer spin chains. The ground-state energies obtained from the exact Bethe ansatz solution for the spin-1/2 chain and the numerical diagonalization on the spin-1, spin-3/2, and spin-2 chains support this prediction.
Soliton dynamics in planar ferromagnets and anti-ferromagnets
Institute of Scientific and Technical Information of China (English)
LINFang-hua; SHATAHJalal
2003-01-01
The aim of this paper is to present a rigorous mathematical proof of the dynamical laws for the topological solitons( magnetic vortices) in ferromagnets and anti-ferromagnets. It is achieved through the conservation laws for the topological vorticity and the weak convergence methods.
Wouters, B; De Nardis, J; Brockmann, M; Fioretto, D; Rigol, M; Caux, J-S
2014-09-12
We study quenches in integrable spin-1/2 chains in which we evolve the ground state of the antiferromagnetic Ising model with the anisotropic Heisenberg Hamiltonian. For this nontrivially interacting situation, an application of the first-principles-based quench-action method allows us to give an exact description of the postquench steady state in the thermodynamic limit. We show that a generalized Gibbs ensemble, implemented using all known local conserved charges, fails to reproduce the exact quench-action steady state and to correctly predict postquench equilibrium expectation values of physical observables. This is supported by numerical linked-cluster calculations within the diagonal ensemble in the thermodynamic limit.
Quantum entanglement in trimer spin-1/2 Heisenberg chains with antiferromagnetic coupling
Del Cima, O M; da Silva, S L L
2015-01-01
The quantum entanglement measure is determined, for the first time, for antiferromagnetic trimer spin-1/2 Heisenberg chains. The physical quantity proposed to measure the entanglement is the distance between states by adopting the Hilbert-Schmidt norm. The method is applied to the new magnetic Cu(II) trimer system, 2b.3CuCl_2.2H_2O, and to the trinuclear Cu(II) halide salt, (3MAP)_2Cu_2Cl_8. The decoherence temperature, above which the entanglement is suppressed, is determined for the both systems. A correlation among their decoherence temperatures and their respective exchange coupling constants is established.
Specific Heat of the Spin-1/2 Antiferromagnetic Heisenberg Chain
Institute of Scientific and Technical Information of China (English)
云国宏; 梁希侠
2001-01-01
A simple analytic theory of thermodynamics at finite temperature for the spin-1/2 antiferromagnetic Heisenberg chain is proposed based on the picture of the particle-hole pair excitations. The dispersion relation of the particle-hole pairs is derived in the formulation of thermodynamic Bethe ansatz provided that the particles and holes have the same energy and they are excited as normalmodes. It is shown that the behaviour of the specific heat is in excellent agreement with the numerical and experimental results.
Energy Technology Data Exchange (ETDEWEB)
Gong, Jia-Min, E-mail: jmgong@yeah.net [School of Electronic Engineering, Xi' an University of Posts and Telecommunications, Xi' an 710121 (China); Tang, Qi [School of Electronic Engineering, Xi' an University of Posts and Telecommunications, Xi' an 710121 (China); Sun, Yu-Hang [School of Science, Xi' an University of Posts and Telecommunications, Xi' an 710121 (China); Qiao, Lin [School of Electronic Engineering, Xi' an University of Posts and Telecommunications, Xi' an 710121 (China)
2015-03-15
We studied the trace distance, the Hellinger distance, and the Bures distance geometric quantum discords (GQDs) for a two-spin Heisenberg XX chain with the Dzyaloshinsky–Moriya (DM) interaction and the external magnetic fields. We found that considerable enhancement of the GQDs can be achieved by introducing the DM interaction, and their maxima were obtained when the strength of the DM interaction approaches infinity. The external magnetic fields and the increase of the temperature can also enhance the GQDs to some extent during certain specific parameter regions.
Paulinelli, H G; de Souza, S M; Rojas, Onofre
2013-07-31
In this paper we explore the entanglement in an orthogonal dimer-plaquette Ising-Heisenberg chain, assembled between plaquette edges, also known as orthogonal dimer plaquettes. The quantum entanglement properties involving an infinite chain structure are quite important, not only because the mathematical calculation is cumbersome but also because real materials are well represented by infinite chains. Using the local gauge symmetry of this model, we are able to map onto a simple spin-1 like Ising and spin-1/2 Heisenberg dimer model with single effective ion anisotropy. Thereafter this model can be solved using the decoration transformation and transfer matrix approach. First, we discuss the phase diagram at zero temperature of this model, where we find five ground states, one ferromagnetic, one antiferromagnetic, one triplet-triplet disordered and one triplet-singlet disordered phase, beside a dimer ferromagnetic-antiferromagnetic phase. In addition, we discuss the thermodynamic properties such as entropy, where we display the residual entropy. Furthermore, using the nearest site correlation function it is possible also to analyze the pairwise thermal entanglement for both orthogonal dimers. Additionally, we discuss the threshold temperature of the entangled region as a function of Hamiltonian parameters. We find a quite interesting thin reentrance threshold temperature for one of the dimers, and we also discuss the differences and similarities for both dimers.
Exact matrix product solutions in the Heisenberg picture of an open quantum spin chain
Energy Technology Data Exchange (ETDEWEB)
Clark, S R; Jaksch, D [Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore); Prior, J [Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU (United Kingdom); Hartmann, M J [Technische Universitaet Muenchen, Physik Department I, James Franck Strasse, 85748 Garching (Germany); Plenio, M B [Institute for Mathematical Sciences, Imperial College London, SW7 2PG (United Kingdom)], E-mail: s.clark@physics.ox.ac.uk
2010-02-15
In recent work, Hartmann et al (2009 Phys. Rev. Lett. 102 057202) demonstrated that the classical simulation of the dynamics of open 1D quantum systems with matrix product algorithms can often be dramatically improved by performing time evolution in the Heisenberg picture. For a closed system this was exemplified by an exact matrix product operator (MPO) solution of the time-evolved creation operator of a quadratic fermi chain with a matrix dimension of just two. In this work, we show that this exact solution can be significantly generalized to include the case of an open quadratic fermi chain subjected to master equation evolution with Lindblad operators that are linear in the fermionic operators. Remarkably even in this open system the time evolution of operators continues to be described by MPOs with the same fixed dimension as that required by the solution of a coherent quadratic fermi chain for all times. Through the use of matrix product algorithms the dynamical behaviour of operators in this non-equilibrium open quantum system can be computed with a cost that is linear in the system size. We present some simple numerical examples that highlight how useful this might be for the more detailed study of open system dynamics. Given that Heisenberg picture simulations have been demonstrated to offer significant accuracy improvements for other open systems that are not exactly solvable, our work also provides further insight into how and why this advantage arises.
Driven isotropic Heisenberg spin chain with arbitrary boundary twisting angle: exact results.
Popkov, V; Karevski, D; Schütz, G M
2013-12-01
We consider an open isotropic Heisenberg quantum spin chain, coupled at the ends to boundary reservoirs polarized in different directions, which sets up a twisting gradient across the chain. Using a matrix product ansatz, we calculate the exact magnetization profiles and magnetization currents in the nonequilibrium steady state of a chain with N sites. The magnetization profiles are harmonic functions with a frequency proportional to the twisting angle θ. The currents of the magnetization components lying in the twisting plane and in the orthogonal direction behave qualitatively differently: In-plane steady-state currents scale as 1/N^{2} for fixed and sufficiently large boundary coupling, and vanish as the coupling increases, while the transversal current increases with the coupling and saturates to 2θ/N.
Hida, Kazuo
2007-02-01
The ground state properties of the high spin Heisenberg chains with alternating single site anisotropy are investigated by means of the numerical exact daigonaization and DMRG method. It is found that the ferrimagnetic state appears between the Haldane phase and period doubled Néel phase for the integer spin chains. On the other hand, the transition from the Tomonaga-Luttinger liquid state into the ferrimagnetic state takes place for the half-odd-integer spin chains. In the ferrimagnetic phase, the spontaneous magnetization varies continuously with the modulation amplitude of the single site anisotropy. Eventually, the magnetization is locked to fractional values of the saturated magnetization. These fractional values satisfy the Oshikawa-Yamanaka-Affleck condition. The local spin profile is calculated to reveal the physical nature of each state. In contrast to the case of frustration induced ferrimagnetism, no incommensurate magnetic superstructure is found.
Spin structure factors of Heisenberg spin chain in the presence of anisotropy and magnetic field
Rezania, H.
2017-02-01
We have theoretically studied the spin structure factors of spin chain in the presence of longitudinal field and transverse anisotropy. The possible effects of easy axis magnetization are investigated in terms of anisotropy in the Heisenberg interactions. This anisotropy is considered for exchange coupling constants perpendicular to magnetic field direction. The original spin model hamiltonian is mapped to a bosonic model via a hard core bosonic transformation where an infinite hard core repulsion is imposed to constrain one boson occupation per site. Using Green's function approach, the energy spectrum of quasiparticle excitation has been obtained. The spectrum of the bosonic gas has been implemented in order to obtain two particle propagator which corresponds to spin structure factor of original Heisenberg chain model Hamiltonian. The results show the position of peak in the longitudinal structure factor at fixed value for anisotropy moves to higher frequency with magnetic field. Also the intensity of dynamical structure factor decreases with magnetic field. A small dependence of longitudinal dynamical spin structure factor on the anisotropy is observed for fixed value of magnetic field. Our results show longitudinal static structure factor is found to be monotonically increasing with magnetic field due to increase of spins aligning along magnetic field. Furthermore the dispersion behaviors of static longitudinal and transverse structure factors for different magnetic fields and anisotropy parameters are addressed.
Quantum vs Classical Magnetization Plateaus of S=1/2 Frustrated Heisenberg Chains
Hida, Kazuo; Affleck, Ian
2005-06-01
The competition between quantum and classical magnetization plateaus of S=1/2 frustrated Heisenberg chains with modified exchange couplings is investigated. The conventional S=1/2 frustrated Heisenberg chain is known to exhibit a 3-fold degenerate \\uparrow\\downarrow\\uparrow-type classical plateau at 1/3 of the saturation magnetization accompanied by the spontaneous Z3 translational symmetry breakdown. The stability of this plateau phase against period 3 exchange modulation which favors the \\bullet\\hskip -1pt-\\hskip -1pt\\bullet \\uparrow-type quantum plateau state (\\bullet\\hskip -1pt-\\hskip -1pt\\bullet = singlet dimer) is studied by bosonization, renormalization group and numerical diagonalization methods. The ground state phase diagram and the spin configuration in each phase are numerically determined. The translationally invariant Valence Bond Solid-type model with 4-spin and third neighbor interactions, which has the exact \\bullet\\hskip -1pt-\\hskip -1pt\\bullet \\uparrow-type quantum plateau state, is also presented. The phase transition to the classical \\uparrow\\downarrow\\uparrow-type ground state is also observed by varying the strength of 4-spin and third neighbor interactions. The relation between these two types of models with quantum plateau states is discussed.
Ground-State Phase Diagram of S = 2 Heisenberg Chains with Alternating Single-Site Anisotropy
Hida, Kazuo
2014-03-01
The ground-state phase diagram of S = 2 antiferromagnetic Heisenberg chains with coexisting uniform and alternating single-site anisotropies is investigated by the numerical exact diagonalization and density matrix renormalization group methods. We find the Haldane, large-D, Néel, period-doubled Néel, gapless spin fluid, quantized and partial ferrimagnetic phases. The Haldane phase is limited to the close neighborhood of the isotropic point. Within numerical accuracy, the transition from the gapless spin-fluid phase to the period-doubled Néel phase is a direct transition. Nevertheless, the presence of a narrow spin-gap phase between these two phases is suggested on the basis of the low-energy effective theory. The ferrimagnetic ground state is present in a wide parameter range. This suggests the realization of magnetized single-chain magnets with a uniform spin magnitude by controlling the environment of each magnetic ion without introducing ferromagnetic interactions.
Quantum Teleportation via Completely Anisotropic Heisenberg Chain in Inhomogeneous Magnetic Field
Institute of Scientific and Technical Information of China (English)
FU Cheng-Hua; HU Zhan-Ning
2013-01-01
The quantum teleportation with the entangled thermal state is investigated based on the completely anisotropic Heisenberg chain in the presence of the externally inhomogeneous magnetic field.The effects of the anisotropy and magnetic field for the quantum fidefity are studied in detail.The zero temperature limit and the features of the nonzero temperature for this nonclassical fidelity are obtained.We find that the quantum teleportation demands more stringent conditions than the thermal entanglement of the resource by investigating the threshold temperature of the thermal concurrence and the critical temperature of the maximal teleportation fidelity.The useful quantum teleportation should avoid the point of the phase transition of the system and the anisotropy of the chain and the external magnetic field can control the applicability of the resource in the quantum teleportation.
Long range anti-ferromagnetic spin model for prebiotic evolution
Energy Technology Data Exchange (ETDEWEB)
Nokura, Kazuo [Shonan Institute of Technology, Fujisawa 251-8511 (Japan)
2003-11-28
I propose and discuss a fitness function for one-dimensional binary monomer sequences of macromolecules for prebiotic evolution. The fitness function is defined by the free energy of polymers in the high temperature random coil phase. With repulsive interactions among the same kind of monomers, the free energy in the high temperature limit becomes the energy function of the one-dimensional long range anti-ferromagnetic spin model, which is shown to have a dynamical phase transition and glassy states.
Analytical and numerical studies of disordered spin-1 Heisenberg chains with aperiodic couplings
Casa Grande, H. L.; Laflorencie, N.; Alet, F.; Vieira, A. P.
2014-04-01
We investigate the low-temperature properties of the one-dimensional spin-1 Heisenberg model with geometric fluctuations induced by aperiodic but deterministic coupling distributions, involving two parameters. We focus on two aperiodic sequences, the Fibonacci sequence and the 6-3 sequence. Our goal is to understand how these geometric fluctuations modify the physics of the (gapped) Haldane phase, which corresponds to the ground state of the uniform spin-1 chain. We make use of different adaptations of the strong-disorder renormalization-group (SDRG) scheme of Ma, Dasgupta, and Hu, widely employed in the study of random spin chains, supplemented by quantum Monte Carlo and density-matrix renormalization-group numerical calculations, to study the nature of the ground state as the coupling modulation is increased. We find no phase transition for the Fibonacci chain, while we show that the 6-3 chain exhibits a phase transition to a gapless, aperiodicity-dominated phase similar to the one found for the aperiodic spin-1/2 XXZ chain. Contrary to what is verified for random spin-1 chains, we show that different adaptations of the SDRG scheme may lead to different qualitative conclusions about the nature of the ground state in the presence of aperiodic coupling modulations.
Isotropic non-Heisenberg behavior in M3(dpa)4Cl2 extended metal atom chains.
Tabookht, Zahra; López, Xavier; Bénard, Marc; de Graaf, Coen
2010-11-25
Isotropic deviations to the standard Heisenberg Hamiltonian have been extracted for a series of trinuclear extended metal atom chain complexes, namely, [Ni(3)(dpa)(4)Cl(2)], and the hypothetical [NiPdNi(dpa)(4)Cl(2)] and [Pd(3)(dpa)(4)Cl(2)], following a scheme recently proposed by Labéguerie and co-workers (J. Chem. Phys 2008, 129, 154110) within the density functional theory framework. Energy calculations of broken symmetry monodeterminantal solutions of intermediate M(s,tot.) values can provide an estimate of the magnitude of the biquadratic exchange interaction (λ) that accounts for these deviations in systems with S = 1 magnetic sites. With the B3LYP functional, we obtain λ = 1.37, 13.8, and 498 cm(-1) for the three molecules, respectively, meaning that a simple Heisenberg Hamiltonian is enough for describing the magnetic behavior of the Ni(3) complex but definitely not for Pd(3). In the latter case, the origin of such extreme deviation arises from (i) an energetically affordable local non-Hund state (small intrasite exchange integral, K ∼ 1960 cm(-1)) and (ii) a very effective overlap between Pd-4d orbitals and a large J. Furthermore, this procedure enables us to determine the relative weights of the two types of magnetic interactions, σ- and δ-like, that contribute to the total magnetic exchange (J = J(σ) + J(δ)). In all of the systems, J is governed by the σ interaction by 95-98%.
Lari, Behzad
2011-01-01
This is a thesis submitted to university of Pune, India, for the Ph.D. degree. This work deals with entanglement production in two qubit, two qutrit and three qubit systems, entanglement in indistinguishable fermionic systems, quantum discord in a Heisenberg chain and geometric measure of quantum discord in an arbitrary state of a bipartite quantum system.
Bagchi, Debarshee
2013-12-11
Using computer simulation we investigate thermal transport in a two segment classical Heisenberg spin chain with nearest neighbor interaction and in the presence of an external magnetic field. The system is thermally driven by heat baths attached at the two ends and transport properties are studied using energy conserving dynamics. We demonstrate that by properly tuning the parameters thermal rectification can be achieved-the system behaves as a good conductor of heat along one direction but becomes a bad conductor when the thermal gradient is reversed, and crucially depends on nonlinearity and spatial asymmetry. Moreover, suitable tuning of the system parameters gives rise to the counterintuitive and technologically important feature known as negative differential thermal resistance (NDTR). We find that the crucial factor responsible for the emergence of NDTR is a suitable mechanism for impeding the current in the bulk of the system.
Correlation functions of XX0 Heisenberg chain, q-binomial determinants, and random walks
Energy Technology Data Exchange (ETDEWEB)
Bogoliubov, N.M.; Malyshev, C.
2014-02-15
The XX0 Heisenberg model on a cyclic chain is considered. The representation of the Bethe wave functions via the Schur functions allows to apply the well-developed theory of the symmetric functions to the calculation of the thermal correlation functions. The determinantal expressions of the form-factors and of the thermal correlation functions are obtained. The q-binomial determinants enable the connection of the form-factors with the generating functions both of boxed plane partitions and of self-avoiding lattice paths. The asymptotical behavior of the thermal correlation functions is studied in the limit of low temperature provided that the characteristic parameters of the system are large enough.
Correlation Functions of XX0 Heisenberg Chain, q-Binomial Determinants, and Random Walks
Bogoliubov, N M
2014-01-01
The XX0 Heisenberg model on a cyclic chain is considered. The representation of the Bethe wave functions via the Schur functions allows to apply the well-developed theory of the symmetric functions to the calculation of the thermal correlation functions. The determinantal expressions of the form-factors and of the thermal correlation functions are obtained. The q-binomial determinants enable the connection of the form-factors with the generating functions both of boxed plane partitions and of self-avoiding lattice paths. The asymptotical behavior of the thermal correlation functions is studied in the limit of low temperature provided that the characteristic parameters of the system are large enough.
Optimal Control for Fast and Robust Generation of Entangled States in Anisotropic Heisenberg Chains
Zhang, Xiong-Peng; Shao, Bin; Zou, Jian
2017-02-01
Motivated by some recent results of the optimal control (OC) theory, we study anisotropic XXZ Heisenberg spin-1/2 chains with control fields acting on a single spin, with the aim of exploring how maximally entangled state can be prepared. To achieve the goal, we use a numerical optimization algorithm (e.g., the Krotov algorithm, which was shown to be capable of reaching the quantum speed limit) to search an optimal set of control parameters, and then obtain OC pulses corresponding to the target fidelity. We find that the minimum time for implementing our target state depending on the anisotropy parameter Δ of the model. Finally, we analyze the robustness of the obtained results for the optimal fidelities and the effectiveness of the Krotov method under some realistic conditions.
Doped Heisenberg chains: Spin-S generalizations of the supersymmetric t-J model
Energy Technology Data Exchange (ETDEWEB)
Frahm, Holger E-mail: frahm@itp.uni-hannover.de
1999-10-25
A family of exactly solvable models describing a spin S Heisenberg chain doped with mobile spin-(S - ((1)/(2))) carriers is constructed from gl(2|1)-invariant solutions of the Yang-Baxter equation. The models are generalizations of the supersymmetric t-J model which is obtained for S ((1)/(2)). We solve the model by means of the algebraic Bethe Ansatz and present results for the zero temperature and thermodynamic properties. At low temperatures the models show spin charge separation, i.e. contain contributions of a free bosonic theory in the charge sector and an SU(2)-invariant theory describing the magnetic excitations. For small carrier concentration the latter can be decomposed further into an SU(2) level-2S Wess-Zumino-Novikov-Witten model and the minimal unitary model M{sub p} with p 2S + 1.
Effects of impurity on the entanglement of the three-qubit Heisenberg XXX spin chain
Institute of Scientific and Technical Information of China (English)
2007-01-01
We investigate the entanglement of the three-qubit Heisenberg XXX chain in the presence of impurity and obtain the analytical expressions of the concurrence C. It is found that for impurity entanglement, C appears only when J1 > J for J > 0, and J1 > 0 for J < 0, and in these two regions C increases with the increase of J1, so is the critical temperature Tc. When J1 >>|J| , C reaches its maximum value 0.5 and Tc reaches the asymptotic value Tc = 3.41448J1. For entanglement between the normal lattices, C appears only when J > 0 and 2J < J1 < J, and initially increases with the increase of J1 and arrives at the maximum value Cmax = (e4JIT-3)/(e4JIT+3) before it decays to zero gradually, so is the critical temperature Tc with, however, the maximum value Tcmax = 4J/ln3.
Ferrimagnetic states in S = 1/2 frustrated Heisenberg chains with period 3 exchange modulation
Hida, K.
2007-04-01
The ground state properties of the S = 1/2 frustrated Heisenberg chain with period 3 exchange modulation are investigated using the numerical diagonalization and density matrix renormalization group (DMRG) method. It is known that this model has a magnetization plateau at one third of the saturation magnetization Ms. On the other hand, the ground state is ferrimagnetic even in the absence of frustration if one of the nearest neighbour bond is ferromagnetic and the others are antiferromagnetic. In the present work, we show that this ferrimagnetic state continues to the region in which all bonds are antiferromagnetic if the frustration is strong. This state further continues to the above-mentioned 1/3 plateau state. In between, we also find the noncollinear ferrimagnetic phase in which the spontaneous magnetization is finite but less than Ms/3. The intuitive interpretation for the phase diagram is given and the physical properties of these phases are discussed.
Ferrimagnetic states in S = 1/2 frustrated Heisenberg chains with period 3 exchange modulation
Energy Technology Data Exchange (ETDEWEB)
Hida, K [Divison of Material Science, Graduate School of Science and Engineering, Saitama University, Saitama, Saitama, 338-8570 (Japan)
2007-04-11
The ground state properties of the S = 1/2 frustrated Heisenberg chain with period 3 exchange modulation are investigated using the numerical diagonalization and density matrix renormalization group (DMRG) method. It is known that this model has a magnetization plateau at one third of the saturation magnetization M{sub s}. On the other hand, the ground state is ferrimagnetic even in the absence of frustration if one of the nearest neighbour bond is ferromagnetic and the others are antiferromagnetic. In the present work, we show that this ferrimagnetic state continues to the region in which all bonds are antiferromagnetic if the frustration is strong. This state further continues to the above-mentioned 1/3 plateau state. In between, we also find the noncollinear ferrimagnetic phase in which the spontaneous magnetization is finite but less than M{sub s}/3. The intuitive interpretation for the phase diagram is given and the physical properties of these phases are discussed.
Sudden Death, Birth and Stable Entanglement in a Two-Qubit Heisenberg XY Spin Chain
Institute of Scientific and Technical Information of China (English)
SHAN Chuan-Jia; CHENG Wei-Wen; LIU Tang-Kun; LIU Ji-Bing; WEI Hua
2008-01-01
Taking the decoherence effect due to population relaxation into account, we investigate the entanglement properties for two qubits in the Heisenberg XY interaction and subject to an external magnetic field. It is found that the phenomenon of entanglement sudden death (ESD) as well as sudden birth (ESB) appear during the evolution process for particular initial states. The influence of the external magnetic field and the spin environment on ESD and ESB are addressed in detail. It is shown that the concurrence, a measure of entanglement, can be controlled by tuning the parameters of the spin chain, such as the anisotropic parameter, external magnetic field, and the coupling strength with their environment. In particular, we find that a critical anisotropy constant exists, above which ESB vanishes while ESD appears. It is also notable that stable entanglement, which is independent of different initial states of the qubits, occurs even in the presence or decoherence.
Thermodynamics of a spin-1/2 XYZ Heisenberg chain with a Dzyaloshinskii-Moriya interaction
Xi, Bin; Hu, Shijie; Luo, Qiang; Zhao, Jize; Wang, Xiaoqun
2017-01-01
We study the thermodynamics of a spin-1/2 XYZ Heisenberg chain with a Dzyaloshinskii-Moriya interaction. This model describes the low-energy behaviors of a one-dimensional two-component bosonic model with a synthetic spin-orbit coupling in the deep insulating region. In the limit U'/U →∞ , where U is the strength of the onsite intracomponent repulsion and U' is the intercomponent one, we solve our model exactly by Jordan-Wigner transformation, and thus provide a benchmark for our following numerical approach. In other cases, we calculate the entropy and the specific heat numerically by the transfer-matrix renormalization-group method. Their low-temperature behaviors depend crucially on the properties of the zero-temperature phases. A refined ground-state phase diagram is then deduced from their low-temperature behaviors. Our findings offer an alternative way to detect those distinguishable phases experimentally.
Partition function zeros and magnetization plateaus of the spin-1 Ising-Heisenberg diamond chain
Hovhannisyan, V. V.; Ananikian, N. S.; Kenna, R.
2016-07-01
We study the properties of the generalized spin-1 Ising-Heisenberg model on a diamond chain, which can be considered as a theoretical model for the homometallic magnetic complex [Ni3(C4H2O4)2 -(μ3 - OH) 2(H2O)4 ] n ṡ(2H2 O) n. The model possesses a large variety of ground-state phases due to the presence of biquadratic and single-ion anisotropy parameters. Magnetization and quadrupole moment plateaus are observed at one- and two-thirds of the saturation value. The distributions of Yang-Lee and Fisher zeros are studied numerically for a variety of values of the model parameters. The usual value σ = -1/2 alongside an unusual value σ = -2/3 is determined for the Yang-Lee edge singularity exponents.
Kosevich, Yuriy A; Gann, Vladimir V
2013-06-19
We study the localization of magnon states in finite defect-free Heisenberg spin-1/2 ferromagnetic chains placed in an inhomogeneous magnetic field with a constant spatial gradient. Continuous transformation from the extended magnon states to the localized Wannier-Zeeman states in a finite spin chain placed in an inhomogeneous field is described both analytically and numerically. We describe for the first time the non-monotonic dependence of the energy levels of magnons, both long and short wavelength, on the magnetic field gradient, which is a consequence of magnon localization in a finite spin chain. We show that, in contrast to the destruction of the magnon band and the establishment of the Wannier-Stark ladder in a vanishingly small field gradient in an infinite chain, the localization of magnon states at the chain ends preserves the memory of the magnon band. Essentially, the localization at the lower- or higher-field chain end resembles the localization of the positive- or negative-effective-mass band quasiparticles. We also show how the beat dynamics of coherent superposition of extended spin waves in a finite chain in a homogeneous or weakly inhomogeneous field transforms into magnon Bloch oscillations of the superposition of localized Wannier-Zeeman states in a strongly inhomogeneous field. We provide a semiclassical description of the magnon Bloch oscillations and show that the correspondence between the quantum and semiclassical descriptions is most accurate for Bloch oscillations of the magnon coherent states, which are built from a coherent superposition of a large number of the nearest-neighbour Wannier-Zeeman states.
Hida, Kazuo
2016-02-01
The topological classification of a series of frustration-induced spin-gap phases in the spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain with next-nearest-neighbour interaction reported in J. Phys. Soc. Jpn. 82, 064703 (2013) is confirmed using two kinds of entanglement spectra defined by different divisions of the whole chain. For the numerical calculation, the iDMRG method is used. The results are consistent with the valence bond solid picture proposed in the previous paper.
Exactly solved mixed spin-(1,1/2) Ising–Heisenberg diamond chain with a single-ion anisotropy
Energy Technology Data Exchange (ETDEWEB)
Lisnyi, Bohdan, E-mail: lisnyj@icmp.lviv.ua [Department of Theoretical Physics and Astrophysics, Faculty of Science, P.J. Šafárik University, Park Angelinum 9, 040 01 Košice (Slovakia); Institute for Condensed Matter Physics, National Academy of Sciences of Ukraine, 1 Svientsitskii Street, 79011 L' viv (Ukraine); Strečka, Jozef, E-mail: jozef.strecka@upjs.sk [Department of Theoretical Physics and Astrophysics, Faculty of Science, P.J. Šafárik University, Park Angelinum 9, 040 01 Košice (Slovakia)
2015-03-01
The mixed spin-(1,1/2) Ising–Heisenberg diamond chain with a single-ion anisotropy is exactly solved through the generalized decoration–iteration transformation and the transfer-matrix method. The decoration–iteration transformation is first used for establishing a rigorous mapping equivalence with the corresponding spin-1 Blume–Emery–Griffiths chain, which is subsequently exactly treated within the transfer-matrix technique. Apart from three classical ground states the model exhibits three striking quantum ground states in which a singlet-dimer state of the interstitial Heisenberg spins is accompanied either with a frustrated state or a polarized state or a non-magnetic state of the nodal Ising spins. It is evidenced that two magnetization plateaus at zero and/or one-half of the saturation magnetization may appear in low-temperature magnetization curves. The specific heat may display remarkable temperature dependences with up to three and four distinct round maxima in a zero and non-zero magnetic field, respectively. - Highlights: • Mixed spin-(1,1/2) Ising–Heisenberg diamond chain is exactly solved. • Quantum ground states with a singlet-dimer state of the Heisenberg spins are found. • Magnetization curve displays intermediate plateaus at zero and half of full magnetization. • Thermal dependences of specific heat may display up to four distinct peaks.
Exact matrix product solutions in the Heisenberg picture of an open quantum spin chain
Clark, S R; Hartmann, M J; Jaksch, D; Plenio, M B
2009-01-01
In recent work Hartmann et al [Phys. Rev. Lett. 102, 057202 (2009)] demonstrated that the classical simulation of the dynamics of open 1D quantum systems with matrix product algorithms can often be dramatically improved by performing time evolution in the Heisenberg picture. For a closed system this was exemplified by an exact matrix product operator solution of the time-evolved creation operator of a quadratic fermi chain with a matrix dimension of just two. In this work we show that this exact solution can be significantly generalized to include the case of an open quadratic fermi chain subjected to master equation evolution with Lindblad operators that are linear in the fermionic operators. Remarkably even in this open system the time-evolution of operators continues to be described by matrix product operators with the same fixed dimension as that required by the solution of a coherent quadratic fermi chain for all times. Through the use of matrix product algorithms the dynamical behaviour of operators in ...
Trapped-ion quantum simulation of tunable-range Heisenberg chains
Energy Technology Data Exchange (ETDEWEB)
Grass, Tobias [ICFO-Institut de Ciencies Fotoniques, Castelldefels, Barcelona (Spain); Lewenstein, Maciej [ICFO-Institut de Ciencies Fotoniques, Castelldefels, Barcelona (Spain); ICREA-Institucio Catalana de Recerca i Estudis Avancats, Barcelona (Spain)
2014-12-01
Quantum-optical techniques allow for generating controllable spin-spin interactions between ions, making trapped ions an ideal quantum simulator of Heisenberg chains. A single parameter, the detuning of the Raman coupling, allows to switch between ferromagnetic and antiferromagnetic chains, and to modify the range of the interactions. On the antiferromagnetic side, the system can be tuned from an extreme long-range limit, in which any pair of ions interacts with almost equal strength, to interactions with a decay. By exact diagonalization, we study how a system of up to 20 ions behaves upon tuning the interactions. We find that it undergoes a transition from a dimerized state with extremely short-ranged correlations towards a state with quasi long-range order, that is, algebraically decaying correlations. The dynamical evolution of the system after a local quench is shown to strongly vary in the two regimes: While in the dimerized limit, the excitation remains localized for long times, propagating spinons characterize the dynamics of the quasi-long-range ordered system. Taking a look onto the ferromagnetic side of the system, we demonstrate the feasibility of witnessing non-locality of quantum correlations by measuring two-particle correlators. (orig.)
Sahoo, Shaon; Durga Prasad Goli, V M L; Sen, Diptiman; Ramasesha, S
2014-07-09
We study Heisenberg spin-1/2 and spin-1 chains with alternating ferromagnetic (J(F)(1)) and antiferromagnetic (J(A)(1)) nearest-neighbor interactions and a ferromagnetic next-nearest-neighbor interaction (J(F)(2)). In this model frustration is present due to the non-zero J(F)(2). The model with site spin s behaves like a Haldane spin chain, with site spin 2s in the limit of vanishing J(F)(2)and large J(F)(1)/J(A)(1). We show that the exact ground state of the model can be found along a line in the parameter space. For fixed J(F)(1), the phase diagram in the space of J(A)(1)-J(F)(2) is determined using numerical techniques complemented by analytical calculations. A number of quantities, including the structure factor, energy gap, entanglement entropy and zero temperature magnetization, are studied to understand the complete phase diagram. An interesting and potentially important feature of this model is that it can exhibit a macroscopic magnetization jump in the presence of a magnetic field; we study this using an effective Hamiltonian.
Strečka, Jozef; Rojas, Onofre; Verkholyak, Taras; Lyra, Marcelo L
2014-02-01
The frustrated spin-1/2 Ising-Heisenberg ladder with Heisenberg intra-rung and Ising inter-rung interactions is exactly solved in a longitudinal magnetic field by taking advantage of the local conservation of the total spin on each rung and the transfer-matrix method. We have rigorously calculated the ground-state phase diagram, magnetization process, magnetocaloric effect, and basic thermodynamic quantities for the model, which can be alternatively viewed as an Ising-Heisenberg tetrahedral chain. It is demonstrated that a stepwise magnetization curve with an intermediate plateau at half of the saturation magnetization is also reflected in respective stepwise changes of the concurrence serving as a measure of bipartite entanglement. The ground-state phase diagram and zero-temperature magnetization curves of the Ising-Heisenberg tetrahedral chain are contrasted with the analogous results of the purely quantum Heisenberg tetrahedral chain, which have been obtained through density-matrix renormalization group (DMRG) calculations. While both ground-state phase diagrams fully coincide in the regime of weak inter-rung interaction, the purely quantum Heisenberg tetrahedral chain develops Luttinger spin-liquid and Haldane phases for strongly coupled rungs, which are absent in the Ising-Heisenberg counterpart model.
Shu, Yu-Rong; Yao, Dao-Xin; Ke, Chih-Wei; Lin, Yu-Cheng; Sandvik, Anders W.
2016-11-01
We use a strong-disorder renormalization group (SDRG) method and ground-state quantum Monte Carlo (QMC) simulations to study S =1 /2 spin chains with random couplings, calculating disorder-averaged spin and dimer correlations. The QMC simulations demonstrate logarithmic corrections to the power-law decaying correlations obtained with the SDRG scheme. The same asymptotic forms apply both for systems with standard Heisenberg exchange and for certain multispin couplings leading to spontaneous dimerization in the clean system. We show that the logarithmic corrections arise in the valence-bond (singlet pair) basis from a contribution that cannot be generated by the SDRG scheme. In the model with multispin couplings, where the clean system dimerizes spontaneously, random singlets form between spinons localized at domain walls in the presence of disorder. This amorphous valence-bond solid is asymptotically a random-singlet state and only differs from the random-exchange Heisenberg chain in its short-distance properties.
NMR evidence for peculiar spin gaps in a doped S=1/2 Heisenberg spin chain
Energy Technology Data Exchange (ETDEWEB)
Utz, Yannic; Rudisch, Christian; Hammerath, Franziska; Grafe, Hans-Joachim; Mohan, Ashwin; Ribeiro, Patrick; Hess, Christian; Wolter, Anja; Kataev, Vladislav; Nishimoto, Satoshi; Drechsler, Stefan-Ludwig; Buechner, Bernd [IFW Dresden (Germany); Singh, Surjeet [Indian Institute of Science Education and Research, Pune (India); Saint-Martin, Romuald; Revcolevschi, Alexandre [Laboratoire de Physico-Chimie de l' Etat Solide, Universite Paris-Sud, Orsay (France)
2012-07-01
We present {sup 63}Cu Nuclear Magnetic Resonance (NMR) measurements on undoped, Ca-doped and Ni-doped SrCuO{sub 2} single crystals. SrCuO{sub 2} is a good realization of a one-dimensional S=1/2 Heisenberg spin chain. This is manifested by the theoretically-expected temperature-independent NMR spin-lattice relaxation rate T{sub 1}{sup -1}. In Sr{sub 0.9}Ca{sub 0.1}CuO{sub 2} an exponential decrease of T{sub 1}{sup -1} below 90 K evidences the opening of a gap in the spin excitation spectrum, which amounts to {Delta}=50 K. DMRG calculations are presented to discuss the origin of this spin gap. New results on SrCu{sub 0.99}Ni{sub 0.01}O{sub 2} also indicate the presence of a spin gap, which is twice as large as in Sr{sub 0.9}Ca{sub 0.1}CuO{sub 2}, despite the minor doping level of Ni compared to Ca. We discuss different possible impacts of Ca (S=0) and Ni (S=1) doping on structural and magnetic properties of the parent compound.
Surface-embeddability approach to the dynamics of the inhomogeneous Heisenberg spin chain
Balakrishnan, Radha; Guha, Partha
1996-08-01
The surface-embeddability approach of Lund and Regge is applied to the classical, inhomogeneous Heisenberg spin chain to study the class of inhomogeneity functions f for which the spin evolution equation and its gauge-equivalent generalized nonlinear Schrödinger equation (GNLSE) are exactly solvable. Writing the spin vector S(x,t) as ∂xr and identifying r(x,t) with a position vector generating a surface, we show that the kinematic equation satisfied by r implies certain constraints on the admissible geometries of this surface. These constraints, together with the Gauss-Mainardi-Codazzi equations, enable us to express the coefficient of the second fundamental form as well as f in terms of the metric coefficients G and its derivatives, for arbitrary time-independent G. Explicit solutions for the GNLSE can also be found in terms of the same quantities. Of the admissible surfaces generated by r, a special class that emerges naturally is that of surfaces of revolution: Explicit solutions for r and S are found and discussed for this class of surfaces.
Effects of impurity on the entanglement of the three-qubit Heisenberg XXX spin chain
Institute of Scientific and Technical Information of China (English)
HU MingLiang; TIAN DongPing
2007-01-01
We investigate the entanglement of the three-qubit Heisenberg XXX chain in the presence of impurity and obtain the analytical expressions of the concurrence C. It is found that for impurity entanglement, C appears only when J1 ＞ J for J ＞ 0, and J1 ＞ 0 for J ＜ 0, and in these two regions C increases with the increase of J1, so is the critical temperature Tc. When J1 >> |J|, C reaches its maximum value 0.5 and Tc reaches the asymptotic value Tc = 3.41448J1. For entanglement between the normal lattices, C appears only when J ＞ 0 and -2J ＜ J1 ＜ J, and initially increases with the increase of J1 and arrives at the maximum value Cmax= (e4J/T-3)/(e4J/T+3) before it decays to zero gradually, so is the critical temperature Tc with, however, the maximum value Tcmax = 4J/In3.
Thermodynamic limit of particle-hole form factors in the massless XXZ Heisenberg chain
Energy Technology Data Exchange (ETDEWEB)
Kitanine, N. [Univ. de Bourgogne (France). IMB, UMR 5584 du CNRS; Kozlowski, K.K. [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany); Maillet, J.M.; Terras, V. [ENS Lyon (France). UMR 5672 du CNRS, Lab. de Physique; Slavnov, N.A. [Steklov Mathematical Inst., Moscow (Russian Federation)
2011-03-15
We study the thermodynamic limit of the particle-hole form factors of the XXZ Heisenberg chain in the massless regime. We show that, in this limit, such form factors decrease as an explicitly computed power-law in the system size. Moreover, the corresponding amplitudes can be obtained as a product of a ''smooth'' and a ''discrete'' part: the former depends continuously on the rapidities of the particles and holes, whereas the latter has an additional explicit dependence on the set of integer numbers that label each excited state in the associated logarithmic Bethe equations. We also show that special form factors corresponding to zero-energy excitations lying on the Fermi surface decrease as a power-law in the system size with the same critical exponents as in the longdistance asymptotic behavior of the related two-point correlation functions. The methods we develop in this article are rather general and can be applied to other massless integrable models associated to the six-vertex R-matrix and having determinant representations for their form factors. (orig.)
Thermodynamic limit of particle-hole form factors in the massless XXZ Heisenberg chain
Kitanine, N; Maillet, J M; Slavnov, N A; Terras, V
2010-01-01
We study the thermodynamic limit of the particle-hole form factors of the XXZ Heisenberg chain in the massless regime. We show that, in this limit, such form factors decrease as an explicitly computed power-law in the system-size. Moreover, the corresponding amplitudes can be obtained as a product of a "smooth" and a "discrete" part: the former depends continuously on the rapidities of the particles and holes, whereas the latter has an additional explicit dependence on the set of integer numbers that label each excited state in the associated logarithmic Bethe equations. We also show that special form factors corresponding to zero-energy excitations lying on the Fermi surface decrease as a power-law in the system size with the same critical exponents as in the long-distance asymptotic behavior of the related two-point correlation functions. The methods we develop in this article are rather general and can be applied to other massless integrable models associated to the six-vertex R-matrix and having determina...
Quantum Phase Transitions in Anti-ferromagnetic Planar Cubic Lattices
Wellard, C J; Wellard, Cameron; Orus, Roman
2004-01-01
Motivated by its relation to an NP-hard problem we analyze the ground state properties of anti-ferromagnetic Ising-spin networks in planar cubic lattices under the action of homogeneous transverse and longitudinal magnetic fields. We consider different instances of the cubic geometry and find a set of quantum phase transitions for each one of the systems, which we characterize by means of entanglement behavior and majorization theory. Entanglement scaling at the critical region is in agreement with results arising from conformal symmetry, therefore even the simplest planar systems can display very large amounts of quantum correlation. No conclusion can be made as to the scaling behavior of the minimum energy gap, with the data allowing equally good fits to exponential and power law decays. Analysis of entanglement and especially of majorization instead of the energy spectrum proves to be a good way of detecting quantum phase transitions in highly frustrated configurations.
DEFF Research Database (Denmark)
Lefmann, K.; Rischel, C.
1996-01-01
We present a numerical diagonalization study of two one-dimensional S=1/2 antiferromagnetic Heisenberg chains, having nearest-neighbor and Haldane-Shastry (1/r(2)) interactions, respectively. We have obtained the T=0 dynamical correlation function, S-alpha alpha(q,omega), for chains of length N=8......-28. We have studied S-zz(q,omega) for the Heisenberg chain in zero field, and from finite-size scaling we have obtained a limiting behavior that for large omega deviates from the conjecture proposed earlier by Muller ct al. For both chains we describe the behavior of S-zz(q,omega) and S...
Sarkar, Subhajit; Chaudhury, Ranjan; Paul, Samir K.
2017-01-01
The available results from the inelastic neutron scattering experiment performed on the quasi-two dimensional spin 1/2 anti-ferromagnetic material La2CuO4 have been analysed theoretically. The formalism of ours is based on a semi-classical like treatment involving a model of an ideal gas of mobile vortices and anti-vortices built on the background of the Néel state, using the bipartite classical spin configuration corresponding to an XY-anisotropic Heisenberg anti-ferromagnet on a square lattice. The results for the integrated intensities for our spin 1/2 model corresponding to different temperatures, show occurrence of vigorous unphysical oscillations, when convoluted with a realistic spectral window function. These results indicate failure of the conventional semi-classical theoretical model of ideal vortex/anti-vortex gas arising in the Berezinskii-Kosterlitz-Thouless theory for the low spin magnetic systems. A full fledged quantum mechanical formalism and calculations seem crucial for the understanding of topological excitations in such low spin systems. Furthermore, a severe disagreement is found to occur at finite values of energy transfer between the integrated intensities obtained theoretically from the conventional formalism and those obtained experimentally. This further suggests strongly that the full quantum treatment should also incorporate the interaction between the fragile-magnons and the topological excitations. This is quite plausible in view of the recent work establishing such a process in XXZ quantum ferromagnet on 2D lattice. The high spin XXZ quasi-two dimensional antiferromagnet like MnPS3 however follows the conventional theory quite well.
Thermal entanglement of a spin-1/2 Ising-Heisenberg model on a symmetrical diamond chain.
Ananikian, N S; Ananikyan, L N; Chakhmakhchyan, L A; Rojas, Onofre
2012-06-27
The entanglement quantum properties of a spin-1/2 Ising-Heisenberg model on a symmetrical diamond chain were analyzed. Due to the separable nature of the Ising-type exchange interactions between neighboring Heisenberg dimers, calculation of the entanglement can be performed exactly for each individual dimer. Pairwise thermal entanglement was studied in terms of the isotropic Ising-Heisenberg model and analytical expressions for the concurrence (as a measure of bipartite entanglement) were obtained. The effects of external magnetic field H and next-nearest neighbor interaction J(m) between nodal Ising sites were considered. The ground state structure and entanglement properties of the system were studied in a wide range of coupling constant values. Various regimes with different values of ground state entanglement were revealed, depending on the relation between competing interaction strengths. Finally, some novel effects, such as the two-peak behavior of concurrence versus temperature and coexistence of phases with different values of magnetic entanglement, were observed.
Exact solution of the mixed spin-1/2 and spin-S Ising-Heisenberg diamond chain
Directory of Open Access Journals (Sweden)
L. Čanová
2009-01-01
Full Text Available The geometric frustration in a class of the mixed spin-1/2 and spin-S Ising-Heisenberg diamond chains is investigated by combining three exact analytical techniques: Kambe projection method, decoration-iteration transformation and transfer-matrix method. The ground state, the magnetization process and the specific heat as a function of the external magnetic field are particularly examined for different strengths of the geometric frustration. It is shown that the increase of the Heisenberg spin value S raises the number of intermediate magnetization plateaux, which emerge in magnetization curves provided that the ground state is highly degenerate on behalf of a sufficiently strong geometric frustration. On the other hand, all intermediate magnetization plateaux merge into a linear magnetization versus magnetic field dependence in the limit of classical Heisenberg spin S → ∞. The enhanced magnetocaloric effect with cooling rate exceeding the one of paramagnetic salts is also detected when the disordered frustrated phase constitutes the ground state and the external magnetic field is small enough.
New Topological Configurations in the Continuous Heisenberg Spin Chain: Lower Bound for the Energy
Directory of Open Access Journals (Sweden)
Rossen Dandoloff
2015-01-01
Full Text Available In order to study the spin configurations of the classical one-dimensional Heisenberg model, we map the normalized unit vector, representing the spin, on a space curve. We show that the total chirality of the configuration is a conserved quantity. If, for example, one end of the space curve is rotated by an angle of 2π relative to the other, the Frenet frame traces out a noncontractible loop in SO(3 and this defines a new class of topological spin configurations for the Heisenberg model.
Maeter, H; Zvyagin, A A; Luetkens, H; Pascua, G; Shermadini, Z; Saint-Martin, R; Revcolevschi, A; Hess, C; Büchner, B; Klauss, H-H
2013-09-11
We report zero and longitudinal magnetic field muon spin relaxation (μSR) measurements of the spin S = 1/2 antiferromagnetic Heisenberg chain material SrCuO2. We find that in a weak applied magnetic field B0 the spin-lattice relaxation rate λ follows a power law λ is proportional to B(0)(-n) with n = 0.9(3). This result is temperature independent for 5 K ≤ T ≤ 300 K. Within conformal field theory and using the Müller ansatz we conclude ballistic spin transport in SrCuO2.
Hida, Kazuo; Chen, Wei
2005-07-01
The effect of spatial modulation of the single-site anisotropy D on the ground state of the S=1 Heisenberg chains is investigated. In the case of period 2 modulation, it is found that the phase diagram contains the Haldane phase, large-D phase, Néel phase of udud-type and u0d0-type. It is shown that the hidden antiferromagnetic order in the Haldane phase compatible with the spatial modulation of D-term get frozen resulting in the emergence of various types of Néel orders. The investigation of the model with longer period D-modulation also confirms this picture.
Magnetocaloric effect in the spin-1/2 Ising-Heisenberg diamond chain with the four-spin interaction
Directory of Open Access Journals (Sweden)
L. Gálisová
2014-03-01
Full Text Available The magnetocaloric effect in the symmetric spin-1/2 Ising–Heisenberg diamond chain with the Ising four-spin interaction is investigated using the generalized decoration-iteration mapping transformation and the transfer-matrix technique. The entropy and the Grüneisen parameter, which closely relate to the magnetocaloric effect, are exactly calculated to compare an ability of the system to cool in the vicinity of different field-induced ground-state phase transitions during the adiabatic demagnetization.
Directory of Open Access Journals (Sweden)
J. Strečka
2012-12-01
Full Text Available The ferrimagnetic spin-1/2 chain composed of alternating Ising and Heisenberg spins in an arbitrarily oriented magnetic field is exactly solved using the spin-rotation transformation and the transfer-matrix method. It is shown that the low-temperature magnetization process depends basically on a spatial orientation of the magnetic field. A sharp stepwise magnetization curve with a marked intermediate plateau, which emerges for the magnetic field applied along the easy-axis direction of the Ising spins, becomes smoother and the intermediate plateau shrinks if the external field is tilted from the easy-axis direction. The magnetization curve of a polycrystalline system is also calculated by performing powder averaging of the derived magnetization formula. The proposed spin-chain model brings an insight into high-field magnetization data of 3d-4f bimetallic polymeric compound Dy(NO3(DMSO2Cu(opba(DMSO2, which provides an interesting experimental realization of the ferrimagnetic chain composed of two different but regularly alternating spin-1/2 magnetic ions Dy3+ and Cu2+ that are reasonably approximated by the notion of Ising and Heisenberg spins, respectively.
Hida, Kazuo
2016-12-01
A series of symmetry-protected topological (SPT) and trivial spin-gap phases in the spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain with alternating next-nearest-neighbour interaction are investigated using two kinds of entanglement spectra defined by different divisions of the whole chain. In case one of the next-nearest-neighbor interactions vanishes, the model reduces to the Δ-chain in which a series of spin-gap phases are found, as shown in J. Phys. Soc. Jpn. 77, 044707 (2008). From the degeneracy of the entanglement spectra, these phases are identified as the SPT and trivial phases. It is found that the ground-state phase boundaries are insensitive to the strength of the alternation in the next-nearest-neighbor interaction. These results are consistent with the analysis based on the nonlinear σ model and exact solution on the ferromagnetic-nonmagnetic phase boundary.
Lorenzana, J.; Eder, R.
1996-01-01
Published in: Phys. Rev. B 55 (1997) 3358-3361 Citing articles (CrossRef) citations recorded in [Science Citation Index] Abstract: We use numerical and analytical results to construct a simple ansatz for the energy dynamical correlation function of the 1D antiferromagnetic Heisenberg model. This is
Law, J M; Benner, H; Kremer, R K
2013-02-13
The temperature dependence of the spin susceptibilities of S = 1, 3/2, 2, 5/2 and 7/2 Heisenberg antiferromagnetic 1D spins chains with nearest-neighbor coupling was simulated via quantum Monte Carlo calculations, within the reduced temperature range of 0.005 ≤ T* ≤ 100, and fitted to a Padé approximation with deviations between the simulated and fitted data of the same order of magnitude as or smaller than the quantum Monte Carlo simulation error. To demonstrate the practicality of our theoretical findings, we compare these results with the susceptibility of the well known 1D chain compound TMMC ([(CH(3))(4)N[MnCl(3)
Ground-State and Thermal Entanglement in Three-Spin Heisenberg-XXZ Chain with Three-Spin Interaction
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The entanglement properties of a three-spin X X Z Heisenberg chain with three-spin interaction are studied by means of concurrence of pairwise entanglement. We show that ground-state pairwise entanglement, pairwise thermal entanglement, or quantum phase transition is not present in antiferromagnetic spin chain. For the ferromagnetic case, quantum phase transition takes place at △ = 1 for anisotropic interaction and at some values of three-spin coupling strength, and pairwise thermal entanglement increases when the value of J/T increases and with anisotropic interaction and three-spin interaction decrease. In addition, we find that increasing the anisotropic interaction and the three-spin interaction will decrease critical temperature.
2003-01-01
We study the anisotropic Heisenberg (XYZ) spin-1/2 chain placed in a magnetic field pointing along the x-axis. We use bosonization and a renormalization group analysis to show that the model has a non-trivial fixed point at a certain value of the XY anisotropy a and the magnetic field h. Hence, there is a line of critical points in the (a,h) plane on which the system is gapless, even though the Hamiltonian has no continuous symmetry. The quantum critical line corresponds to a spin-flop transi...
Spin transport of the frustrated integer spin S antiferromagnetic Heisenberg chain
Energy Technology Data Exchange (ETDEWEB)
Lima, Leonardo S., E-mail: lslima@infis.ufu.br [Instituto de Física, Universidade Federal de Uberlândia, UFU, CEP:38700-128, Patos de Minas, MG (Brazil); Departamento de Física, ICEx, Universidade Federal de Minas Gerais, CEP:31270-901, Belo Horizonte, MG (Brazil)
2014-03-15
We study the effect of the nearest-neighbor (nn) and next-nearest-neighbor (nnn) interactions on spin transport in the quantum integer spin one-dimensional isotropic antiferromagnetic Heisenberg model. The Kubo formalism of the linear response theory is used to calculate the spin conductivity. We obtain the regular part of the spin conductivity, σ{sup reg}(ω), as function of the frequency at T=0 and obtain a strong effect of the (nnn) interaction on magnon transport.
Entanglement of a Five-Qubit Heisenberg XX Chain in a Magnetic Field
Institute of Scientific and Technical Information of China (English)
CAO Min; LING Yin-Sheng; ZHU Shi-Qun
2009-01-01
We calculate the eigenvalues and eigenvectors of a five-qubit isotropic Heisenberg model in an external magnetic field, and give analytical results for the concurrence of two nearest-neighbor qubits. A magnetic field can eliminate degeneration and change the ground state of the system. Therefore increasing the value of the magnetic field can induce entanglement in a certain range both for the antiferromagnetic and ferromagnetic case.
Influence of Intrinsic Decoherence on Entanglement in Two-Qubit Quantum Heisenberg XYZ Chain
Institute of Scientific and Technical Information of China (English)
SHAO Bin; ZENG Tian-Hai; ZOU Jian
2005-01-01
Taking the intrinsic decoherence effect into account, we investigate the time evolution of entanglement for two-qubit XYZ Heisenberg model in an external uniform magnetic field. Concurrence, the measurement of entanglement,is calculated. We show how the intrinsic decoherence modifies the time evolution of the entanglement and find that at short-time case, concurrence is oscillating as increasing magnetic field, which implies that entanglement may be enhanced or weakened in some time regions.
Two Qubits Entanglement Dynamics in 1D Heisenberg Chain with Intrinsic Decoherence
Institute of Scientific and Technical Information of China (English)
SHAO Bin; ZHANG Li-li; ZOU Jian
2006-01-01
To reveal how the decoherence modifies the time evolution of the entanglement of quantum system,the intrinsic decoherence approach and the entanglement of formation are used, and the time evolution of entanglement for two-qubit 1D quantum Heisenberg model in an external uniform magnetic field is derived. It is shown that the external magnetic field can strengthen the effects of the intrinsic decoherence on the entanglement of the system.
Broek, van den P.M.
1980-01-01
It is shown that the ground state energy of the hamiltonian H = Σ Si · Si+1 + γΣSi · Si+2 for the linear antiferromagnetic Heisenberg chain with nearest and next-nearest neighbour interactions is equal to -3/2 if γ = 1/2.
飛田, 和男
2008-01-01
Original Paper :Critical Properties of Spin-1 Antiferromagnetic Heisenberg Chains with Bond Alternation and Uniaxial Single-Ion-Type AnisotropyWei Chen, Kazuo Hida and Bryan Clifford Sanctuary Journal of the Physical Society of Japan 69 (2000) pp.237-241
Entanglement dynamics of a Heisenberg chain with Dzyaloshinski-Moriya interaction
Institute of Scientific and Technical Information of China (English)
Zheng qiang; Zhang Xiao-Ping; Zhi Qi-Jun; Ren Zhong-Zhou
2009-01-01
This paper investigates the entanglement dynamics of the system,composed of two qubits A and B with Heisenberg XX spin interactation.There is a third controller qubit C,which only has Dzyaloshiuskii-Moriya (DM) spin-orbit interaction with the qubit B.It is found that depending on the initial state of the controller qubit C and DM interaction,the entanglement of the system displays amplification and sudden birth effects.These effects indicate that one can control the entanglement of the system,which may be helpful for quantum information processing.
Impurity effects in a S=1/2 Heisenberg spin chain probed by {sup 63}Cu NMR
Energy Technology Data Exchange (ETDEWEB)
Utz, Yannic; Bruening, Eva Maria; Hammerath, Franziska; Rudisch, Christian; Grafe, Hans-Joachim; Mohan, Ashwin; Hess, Christian; Nishimoto, Satoshi; Drechsler, Stefan-Ludwig; Buechner, Bernd [IFW Dresden (Germany); Saint-Martin, Romuald; Revcolevschi, Alexandre [LPCES, Orsay (France)
2013-07-01
We present {sup 63}Cu NMR measurements on undoped, Ni doped and Mg doped SrCuO{sub 2} single crystals. SrCuO{sub 2} is a good realization of a one-dimensional S=1/2 Heisenberg spin chain. This is confirmed by the theoretically-expected temperature independent NMR spin-lattice relaxation rate T{sup -1}{sub 1}. Doping with Ni, which can be regarded as a S=1 impurity, has a major impact on the magnetic properties of the spin chains. On the one hand, this is manifested by unusual features in the NMR spectra below 100 K, revealing the existence of an impurity-induced local alternating magnetisation. On the other hand, exponentially decaying spin lattice relaxation rates towards low temperatures indicate the opening of a spin gap similar to Ca doped SrCuO{sub 2}. Mg doping (S=0) has, however, no influence on the magnetic properties of the spin chains. Neither the NMR spectra nor the spin lattice relaxation rates differ from those measured on pure SrCuO{sub 2}. While the different impact of Ni and Mg doping on the spin chains could be explained by their different impurity spins, the opening of a spin gap in case of Ni doping is totally unexpected and not yet understood.
Hovhannisyan, V V; Strečka, J; Ananikian, N S
2016-03-02
The spin-1 Ising-Heisenberg diamond chain with the second-neighbor interaction between nodal spins is rigorously solved using the transfer-matrix method. In particular, exact results for the ground state, magnetization process and specific heat are presented and discussed. It is shown that further-neighbor interaction between nodal spins gives rise to three novel ground states with a translationally broken symmetry, but at the same time, does not increases the total number of intermediate plateaus in a zero-temperature magnetization curve compared with the simplified model without this interaction term. The zero-field specific heat displays interesting thermal dependencies with a single- or double-peak structure.
Effects of Anisotropy on Pair-wise Entanglement of a Four-Qubit Heisenberg X X Z Chain
Institute of Scientific and Technical Information of China (English)
CAO Min; ZHU Shi-Qun
2006-01-01
@@ The pair-wise thermal entanglement in a four-qubit Heisenberg XXZ chain is investigated to study the role of anisotropy when an external magnetic field is included. It is found that pair-wise entanglement is absent between nearest- and next-nearest neighbouring qubits with anisotropic parameter △≤ -1. For two nearest-neighbouring qubits, increasing the parameter can not only induce the entanglement, but also extend the entanglement region in terms of magnetic field B and temperature T. For two next-nearest-neighbouring qubits, increasing anisotropic parameter can shift the location of the entanglement and control the extent of the entanglement in terms of magnetic field at a finite temperature.
Strečka, Jozef; Verkholyak, Taras
2016-10-01
Magnetic properties of the ferrimagnetic mixed spin-(1/2,S) Heisenberg chains are examined using quantum Monte Carlo simulations for two different quantum spin numbers S=1 and 3/2. The calculated magnetization curves at finite temperatures are confronted with zero-temperature magnetization data obtained within the density matrix renormalization group method, which imply an existence of two quantum critical points determining a breakdown of the gapped Lieb-Mattis ferrimagnetic phase and Tomonaga-Luttinger spin-liquid phase, respectively. While a square root behavior of the magnetization accompanying each quantum critical point is gradually smoothed upon rising temperature, the susceptibility and isothermal entropy change data at low temperatures provide a stronger evidence of the zero-temperature quantum critical points through marked local maxima and minima, respectively.
Institute of Scientific and Technical Information of China (English)
Huang Li-Yuan; Fang Mao-Fa
2008-01-01
The thermal entanglement and teleportation of a thermally mixed entangled state of a two-qubit Heisenberg XXX chain under the Dzyaloshinski-Moriya (DM) anisotropic antisymmetric interaction through a noisy quantum channel given by a Werner state is investigated. The dependences of the thermal entanglement of the teleported state on the DM coupling constant, the temperature and the entanglement of the noisy quantum channel are studied in detail for both the ferromagnetic and the antiferromagnetic cases. The result shows that a minimum entanglement of the noisy quantum channel must be provided in order to realize the entanglement teleportation. The values of fidelity of the teleported state are also studied for these two cases. It is found that under certain conditions, we can transfer an initial state with a better fidelity than that for any classical communication protocol.
Multispinon continua at zero and finite temperature in a near-ideal Heisenberg chain.
Lake, B; Tennant, D A; Caux, J-S; Barthel, T; Schollwöck, U; Nagler, S E; Frost, C D
2013-09-27
The space-and time-dependent response of many-body quantum systems is the most informative aspect of their emergent behavior. The dynamical structure factor, experimentally measurable using neutron scattering, can map this response in wave vector and energy with great detail, allowing theories to be quantitatively tested to high accuracy. Here, we present a comparison between neutron scattering measurements on the one-dimensional spin-1/2 Heisenberg antiferromagnet KCuF3, and recent state-of-the-art theoretical methods based on integrability and density matrix renormalization group simulations. The unprecedented quantitative agreement shows that precise descriptions of strongly correlated states at all distance, time, and temperature scales are now possible, and highlights the need to apply these novel techniques to other problems in low-dimensional magnetism.
Gaussian phase transition and critical exponents in spin-1 bond-alternative Heisenberg chains
Su, Yao Heng; Chen, Ai Min; Xiang, Chunhuan; Wang, Honglei; Xia, Cai-Juan; Wang, Jun
2016-12-01
The quantum Gaussian phase transition is investigated for the infinite spin-1 bond-alternative Heisenberg model in one spatial dimension. By using a tensor network representation with an infinite matrix product state approach, the ground state energy, bipartite entanglement entropy, non-local string order, and fidelity per lattice site are calculated to characterize the phase transition. At the quantum phase transition point, the scaling behavior of various physical observables with respect to the finite truncation dimension are discussed for the ground state wavefunctions. In addition, the central charge is extracted from the finite entanglement entropies and the finite correlation lengths. Furthermore, the various critical exponents of the string order are calculated. The characteristic critical exponents and the central charge determine the universality class of the phase transition.
Hida, K.; Affleck, I.
The magnetization plateau of the S = 1/2 frustrated Heisenberg chain with period 3 parity invariant exchange modulation is investigated by the bosonization and numerical exact diagonalization method. The ground state phase diagram at 1/3 of the saturated magnetization is obtained. Among three degenerate \\uparrow\\uparrowdownarrow-type plateau states in the uniform chain, two of them (downarrow\\uparrow\\uparrowdownarrow\\uparrow\\uparrow\\cdots\\ and \\uparrowdownarrow\\uparrow\\uparrowdownarrow\\uparrow\\cdots\\ ) turned out to be robust against the period 3 exchange modulation which favors the bullet-bullet\\uparrowbullet-bullet\\uparrow\\cdots phase up to a critical value of the modulation amplitude (bullet-bullet = singlet dimer) resulting in the Z_2 symmetry broken phase. Another \\uparrow\\uparrowdownarrow-type state with \\uparrow\\uparrowdownarrow\\uparrow\\uparrowdownarrow\\cdots\\ configuration is stabilized for period 3 modulation with opposite sign. The transition between the bullet-bullet\\uparrowbullet-bullet\\uparrow\\cdots\\ -phase and Z_2-broken phase is the Ising transition and that between the \\uparrow\\uparrowdownarrow\\uparrow\\uparrowdownarrow\\cdots\\ -phase and Z_2 broken phase is the first order transition. The spin configuration in each phase is numerically verified by applying the local symmetry breaking field.
Boundary-induced spin-density waves in linear Heisenberg antiferromagnetic spin chains with S ≥1
Dey, Dayasindhu; Kumar, Manoranjan; Soos, Zoltán G.
2016-10-01
Linear Heisenberg antiferromagnets (HAFs) are chains of spin-S sites with isotropic exchange J between neighbors. Open and periodic boundary conditions return the same ground-state energy per site in the thermodynamic limit, but not the same spin SG when S ≥1 . The ground state of open chains of N spins has SG=0 or S , respectively, for even or odd N . Density-matrix renormalization-group calculations with different algorithms for even and odd N are presented up to N =500 for the energy and spin densities ρ (r ,N ) of edge states in HAFs with S =1 , 3/2, and 2. The edge states are boundary-induced spin density waves (BI-SDWs) with ρ (r ,N ) ∝(-1) r -1 for r =1 ,2 ,...,N . The SDWs are in phase when N is odd, are out of phase when N is even, and have finite excitation energy Γ (N ) that decreases exponentially with N for integer S and faster than 1 /N for half integer S . The spin densities and excitation energy are quantitatively modeled for integer S chains longer than 5 ξ spins by two parameters, the correlation length ξ and the SDW amplitude, with ξ =6.048 for S =1 and 49.0 for S =2 . The BI-SDWs of S =3 /2 chains are not localized and are qualitatively different for even and odd N . Exchange between the ends for odd N is mediated by a delocalized effective spin in the middle that increases |Γ (N )| and weakens the size dependence. The nonlinear sigma model (NL σ M ) has been applied to the HAFs, primarily to S =1 with even N , to discuss spin densities and exchange between localized states at the ends as Γ (N ) ∝(-1) Nexp(-N /ξ ) . S =1 chains with odd N are fully consistent with the NL σ M ; S =2 chains have two gaps Γ (N ) with the same ξ as predicted whose ratio is 3.45 rather than 3; the NL σ M is more approximate for S =3 /2 chains with even N and is modified for exchange between ends for odd N .
Singular eigenstates in the even(odd) length Heisenberg spin chain
Giri, Pulak Ranjan
2014-01-01
Introducing a regularization scheme, we derive a set of equations for the rapidities of the singular solutions, whose distinct and self-conjugate solutions produce Bethe eigenstates. We obtain singular eigenstates and their corresponding eigenvalues of the transfer matrix of the spin-1/2 XXX chain. For an even length spin-1/2 XXX chain, we show that the singular solutions \\{\\lambda_\\alpha\\} are invariant under the sign changes of their rapidities, \\{\\lambda_\\alpha\\}=\\{-\\lambda_\\alpha\\}. For odd N length spin-1/2 chain in the three down-spin sector, it has been analytically shown that there exist singular solutions in any finite length of the spin chain of the form N= 3\\left(2k+1\\right) with k=1, 2, 3, \\cdots. It is also shown that there exist no singular solutions in the four down-spin sector for some odd length spin-1/2 XXX chains.
Singular eigenstates in the even(odd) length Heisenberg spin chain
Ranjan Giri, Pulak; Deguchi, Tetsuo
2015-05-01
We study the implications of the regularization for the singular solutions on the even(odd) length spin-1/2 XXX chains in some specific down-spin sectors. In particular, the analytic expressions of the Bethe eigenstates for three down-spin sector have been obtained along with their numerical forms in some fixed length chains. For an even-length chain if the singular solutions \\{{{λ }α }\\} are invariant under the sign changes of their rapidities \\{{{λ }α }\\}=\\{-{{λ }α }\\}, then the Bethe ansatz equations are reduced to a system of (M-2)/2((M-3)/2) equations in an even (odd) down-spin sector. For an odd N length chain in the three down-spin sector, it has been analytically shown that there exist singular solutions in any finite length of the spin chain of the form N=3(2k+1) with k=1,2,3,\\cdots . It is also shown that there exist no singular solutions in the four down-spin sector for some odd-length spin-1/2 XXX chains.
Haghshenas, R; Langari, A; Rezakhani, A T
2014-11-12
We study different phases of the one-dimensional bond-alternating spin-1/2 Heisenberg model by using the symmetry fractionalization mechanism. We employ the infinite matrix-product state representation of the ground state (through the infinite-size density matrix renormalization group algorithm) to obtain inequivalent projective representations and commutation relations of the (unbroken) symmetry groups of the model, which are used to identify the different phases. We find that the model exhibits trivial as well as symmetry-protected topological phases. The symmetry-protected topological phases are Haldane phases on even/odd bonds, which are protected by the time-reversal (acting on the spin as σ → -σ), parity (permutation of the chain about a specific bond), and dihedral (π-rotations about a pair of orthogonal axes) symmetries. Additionally, we investigate the phases of the most general two-body bond-alternating spin-1/2 model, which respects the time-reversal, parity, and dihedral symmetries, and obtain its corresponding twelve different types of the symmetry-protected topological phases.
Local probe of fractional edge states of S=1 Heisenberg spin chains.
Delgado, F; Batista, C D; Fernández-Rossier, J
2013-10-18
Spin chains are among the simplest physical systems in which electron-electron interactions induce novel states of matter. Here we propose to combine atomic scale engineering and spectroscopic capabilities of state of the art scanning tunnel microscopy to probe the fractionalized edge states of individual atomic scale S=1 spin chains. These edge states arise from the topological order of the ground state in the Haldane phase. We also show that the Haldane gap and the spin-spin correlation length can be measured with the same technique.
Hida, Kazuo
2006-07-01
The multiple reentrant quantum phase transitions in the S=1/2 antiferromagnetic Heisenberg chains with random bond alternation in the magnetic field are investigated by the density matrix renormalization group method combined with interchain mean field approximation. It is assumed that odd numbered bonds are antiferromagnetic with strength J and even numbered bonds can take the values JS and JW (JS > J > JW > 0) randomly with the probabilities p and 1- p, respectively. The pure version ( p=0 and 1) of this model has a spin gap but exhibits a field-induced antiferromagnetism in the presence of interchain coupling if Zeeman energy due to the magnetic field exceeds the spin gap. For 0 < p < 1, antiferromagnetism is induced by randomness at the small field region where the ground state is disordered due to the spin gap in the pure version. At the same time, this model exhibits randomness-induced plateaus at several values of magnetization. The antiferromagnetism is destroyed on the plateaus. As a consequence, we find a series of reentrant quantum phase transitions between transverse antiferromagnetic phases and disordered plateau phases with the increase of magnetic field for a moderate strength of interchain coupling. Above the main plateaus, the magnetization curve consists of a series of small plateaus and jumps between them. It is also found that antiferromagnetism is induced by infinitesimal interchain coupling at the jumps between the small plateaus. We conclude that this antiferromagnetism is supported by the mixing of low-lying excited states by the staggered interchain mean field even though the spin correlation function is short ranged in the ground state of each chain.
Spinon and bound-state excitation light cones in Heisenberg XXZ chains
de Paula, A. L.; Bragança, H.; Pereira, R. G.; Drumond, R. C.; Aguiar, M. C. O.
2017-01-01
We investigate the out-of-equilibrium dynamics after a local quench that connects two spin-1/2 XXZ chains prepared in the ground state of the Hamiltonian in different phases, one in the ferromagnetic phase and the other in the critical phase. We analyze the time evolution of the on-site magnetization and bipartite entanglement entropy via adaptive time-dependent density matrix renormalization group. In systems with short-range interactions, such as the one we consider, the velocity of information transfer is expected to be bounded, giving rise to a light-cone effect. Interestingly, our results show that, when the anisotropy parameter of the critical chain is sufficiently close to that of the isotropic ferromagnet, the light cone is determined by the velocity of spin-wave bound states that propagate faster than single-particle ("spinon") excitations. Furthermore, we investigate how the system approaches equilibrium in the inhomogeneous ground state of the connected system, in which the ferromagnetic chain induces a nonzero magnetization in the critical chain in the vicinity of the interface.
The anti-ferromagnetic Ising model on the simplest pure Husimi lattice: An exact solution
Energy Technology Data Exchange (ETDEWEB)
Jurčišinová, E., E-mail: jurcisine@saske.sk [Institute of Experimental Physics, SAS, Watsonova 47, 040 01 Košice (Slovakia); Jurčišin, M., E-mail: jurcisin@saske.sk [Institute of Experimental Physics, SAS, Watsonova 47, 040 01 Košice (Slovakia); Bobák, A., E-mail: andrej.bobak@upjs.sk [Department of Theoretical Physics and Astrophysics, Faculty of Science, P.J. Šafárik University, Park Angelinum 9, 040 01 Košice (Slovakia)
2013-11-22
The anti-ferromagnetic spin-1/2 Ising model on the pure Husimi lattice with three sites in the elementary polygon (p=3) and the coordination number z=4 is investigated. It represents the simplest approximation of the anti-ferromagnetic Ising model on the two-dimensional kagome lattice which takes into account effects of frustration. The exact analytical solution of the model is found and discussed. It is proven that the model does not exhibit the first order as well as the second order phase transitions. A detailed analysis of the magnetization properties is performed and the existence of the magnetization plateaus for low temperatures is shown. All possible ground states of the model are found and discussed.
Quantum breathers in Heisenberg ferromagnetic chains with Dzyaloshinsky-Moriya interaction.
Tang, Bing; Li, De-Jun; Tang, Yi
2014-06-01
We present an analytical study on quantum breathers in one-dimensional ferromagnetic XXZ chains with Dzyaloshinsky-Moriya interaction by means of the time-dependent Hartree approximation and the semidiscrete multiple-scale method. The stationary localized single-boson wave functions are obtained and these analytical solutions are checked by numerical simulations. With such stationary localized single-boson wave functions, we construct quantum breather states. Furthermore, the role of the Dzyaloshinsky-Moriya interaction is discussed.
Quantum breathers in Heisenberg ferromagnetic chains with Dzyaloshinsky-Moriya interaction
Energy Technology Data Exchange (ETDEWEB)
Tang, Bing; Tang, Yi, E-mail: tangyii@hotmail.com [Department of Physics, Xiangtan University, Xiangtan 411105 (China); Li, De-Jun [College of Physics, Mechanical and Electrical Engineering, Jishou University, Jishou 416000 (China)
2014-06-15
We present an analytical study on quantum breathers in one-dimensional ferromagnetic XXZ chains with Dzyaloshinsky-Moriya interaction by means of the time-dependent Hartree approximation and the semidiscrete multiple-scale method. The stationary localized single-boson wave functions are obtained and these analytical solutions are checked by numerical simulations. With such stationary localized single-boson wave functions, we construct quantum breather states. Furthermore, the role of the Dzyaloshinsky-Moriya interaction is discussed.
Adiabatic Evolution in XXX Spin Chain is Fast
Korepin, V
2004-01-01
Adiabatic theorem of quantum mechanics was used by E. Farhi, J. Goldstone, S. Gutmann and M. Sipser to design quantum algorithms of a new kind. A quantum computer evolves slowly enough, so that it remains in its instantaneous ground state, which tells the solution. We consider XXX Heisenberg spin chain. We rotate magnetic field and change its magnitude. The ground state evolves from a ferromagnetic one into a nontrivial ground state of XXX anti-ferromagnet. This adiabatic evolution goes very gently. Because of SU(2) symmetry and integrability only one mode get exited. We prove that the time of the evolution scales as a square root of number of qubits. This is faster then other known examples.
Djoufack, Z. I.; Tala-Tebue, E.; Nguenang, J. P.; Kenfack-Jiotsa, A.
2016-10-01
We report in this work, an analytical study of quantum soliton in 1D Heisenberg spin chains with Dzyaloshinsky-Moriya Interaction (DMI) and Next-Nearest-Neighbor Interactions (NNNI). By means of the time-dependent Hartree approximation and the semi-discrete multiple-scale method, the equation of motion for the single-boson wave function is reduced to the nonlinear Schrödinger equation. It comes from this present study that the spectrum of the frequencies increases, its periodicity changes, in the presence of NNNI. The antisymmetric feature of the DMI was probed from the dispersion curve while changing the sign of the parameter controlling it. Five regions were identified in the dispersion spectrum, when the NNNI are taken into account instead of three as in the opposite case. In each of these regions, the quantum model can exhibit quantum stationary localized and stable bright or dark soliton solutions. In each region, we could set up quantum localized n-boson Hartree states as well as the analytical expression of their energy level, respectively. The accuracy of the analytical studies is confirmed by the excellent agreement with the numerical calculations, and it certifies the stability of the stationary quantum localized solitons solutions exhibited in each region. In addition, we found that the intensity of the localization of quantum localized n-boson Hartree states increases when the NNNI are considered. We also realized that the intensity of Hartree n-boson states corresponding to quantum discrete soliton states depend on the wave vector.
Conductivity in the Heisenberg chain with next-to-nearest-neighbor interaction.
Mastropietro, Vieri
2013-04-01
We consider a spin chain given by the XXZ model with a weak next-to-nearest-neighbor perturbation that breaks its exact integrability. We prove that such a system has an ideal metallic behavior (infinite conductivity), by rigorously establishing strict lower bounds on the zero-temperature Drude weight, which are strictly positive. The proof is based on exact renormalization group methods allowing us to prove the convergence of the expansions and to fully take into account the irrelevant terms, which play an essential role in ensuring the correct lattice symmetries. We also prove that the Drude weight verifies the same parameter-free relations as in the absence of the integrability-breaking perturbation.
Lorenzana, J.; Eder, R
1997-01-01
We use numerical and analytical results to construct a simple ansatz for the energy dynamical correlation function of the one-dimensional antiferromagnetic Heisenberg model. This is applied to compute the phonon-assisted absorption spectra of magnetic excitations (spinons) in quasi-one-dimensional s
DEFF Research Database (Denmark)
Gammelmark, Søren; Mølmer, Klaus
2011-01-01
the Ising phase transition. Physical systems with first-order phase transitions are natural candidates for metrology and calibration purposes, and we apply filter theory to show that the sensitivity of the physical system to temperature and external fields reaches the 1/N Heisenberg limit....
Yannouleas, Constantine; Brandt, Benedikt B.; Landman, Uzi
2016-07-01
Advances with trapped ultracold atoms intensified interest in simulating complex physical phenomena, including quantum magnetism and transitions from itinerant to non-itinerant behavior. Here we show formation of antiferromagnetic ground states of few ultracold fermionic atoms in single and double well (DW) traps, through microscopic Hamiltonian exact diagonalization for two DW arrangements: (i) two linearly oriented one-dimensional, 1D, wells, and (ii) two coupled parallel wells, forming a trap of two-dimensional, 2D, nature. The spectra and spin-resolved conditional probabilities reveal for both cases, under strong repulsion, atomic spatial localization at extemporaneously created sites, forming quantum molecular magnetic structures with non-itinerant character. These findings usher future theoretical and experimental explorations into the highly correlated behavior of ultracold strongly repelling fermionic atoms in higher dimensions, beyond the fermionization physics that is strictly applicable only in the 1D case. The results for four atoms are well described with finite Heisenberg spin-chain and cluster models. The numerical simulations of three fermionic atoms in symmetric DWs reveal the emergent appearance of coupled resonating 2D Heisenberg clusters, whose emulation requires the use of a t-J-like model, akin to that used in investigations of high T c superconductivity. The highly entangled states discovered in the microscopic and model calculations of controllably detuned, asymmetric, DWs suggest three-cold-atom DW quantum computing qubits.
Langari, A; Pollmann, F; Siahatgar, M
2013-10-09
We study the phase diagram of the anisotropic spin-1 Heisenberg chain with single ion anisotropy (D) using a ground-state fidelity approach. The ground-state fidelity and its corresponding susceptibility are calculated within the quantum renormalization group scheme where we obtained the renormalization of fidelity preventing calculation of the ground state. Using this approach, the phase boundaries between the antiferromagnetic Néel, Haldane and large-D phases are obtained for the whole phase diagram, which justifies the application of quantum renormalization group to trace the symmetry-protected topological phases. In addition, we present numerical exact diagonalization (Lanczos) results in which we employ a recently introduced non-local order parameter to locate the transition from Haldane to large-D phase accurately.
Hida, Kazuo; Takano, Ken'ichi; Suzuki, Hidenori
2013-06-01
The spin-1/2 ferromagnetic--antiferromagnetic alternating Heisenberg chain with ferromagnetic next-nearest-neighbour (NNN) interaction is investigated. The ground state is the Haldane phase for weak NNN interaction, and is the ferromagnetic phase for weak antiferromagnetic interaction. We find a series of topologically distinct spin-gap phases with various magnitudes of edge spins for strong NNN interaction. The phase boundaries between these phases are determined on the basis of the DMRG calculation with additional spins that compensate the edge spins. It is found that each of the exact solutions with short-range antiferromagnetic correlation on the ferromagnetic--nonmagnetic phase boundary is representative of each spin gap phase.
Kono, Y; Sakakibara, T; Aoyama, C P; Hotta, C; Turnbull, M M; Landee, C P; Takano, Y
2015-01-23
High-precision dc magnetization measurements have been made on Cu(C4H4N2) (NO3)2 in magnetic fields up to 14.7 T, slightly above the saturation field Hs=13.97 T, in the temperature range from 0.08 to 15 K. The magnetization curve and differential susceptibility at the lowest temperature show excellent agreement with exact theoretical results for the spin-1/2 Heisenberg antiferromagnet in one dimension. A broad peak is observed in magnetization measured as a function of temperature, signaling a crossover to a low-temperature Tomonaga-Luttinger-liquid regime. With an increasing field, the peak moves gradually to lower temperatures, compressing the regime, and, at Hs, the magnetization exhibits a strong upturn. This quantum critical behavior of the magnetization and that of the specific heat withstand quantitative tests against theory, demonstrating that the material is a practically perfect one-dimensional spin-1/2 Heisenberg antiferromagnet.
Energy Technology Data Exchange (ETDEWEB)
Utz, Yannic; Hammerath, Franziska; Nishimoto, Satoshi; Drechsler, Stefan-Ludwig; Hess, Christian; Buechner, Bernd; Grafe, Hans-Joachim [IFW Dresden (Germany); Beesetty, Neela Sekhar; Saint-Martin, Romuald; Revcolevschi, Alexandre [SP2M-ICMMO UMR-CNRS, Universite Paris-Sud (France)
2015-07-01
We present {sup 63}Cu NMR measurements on single crystals of Sr{sub 2}CuO{sub 3} doped with different amounts of nickel and compare them to numerical DMRG results. The parent compound contains copper-oxygen chains with S=1/2 on the copper site coupled by a large antiferromagnetic exchange coupling J ∼ 2000 K and is known to be a good realization of the 1D Heisenberg model. The measurements show that replacing only a few of the S=1/2 Cu ions with S=1 Ni has a major impact on the magnetic properties of the spin chain system. An unusual line broadening in the low temperature NMR spectra reveals the existence of an impurity-induced local alternating magnetization (LAM), and exponentially decaying spin-lattice relaxation rates T{sup -1}{sub 1} towards low temperatures indicate the opening of a spin gap similar to Ca-doped Sr{sub 2}CuO{sub 3}. While the T{sup -1}{sub 1} measurements could be explained by pure chain segmentation, as expected for a S=0 impurity, the spectra can only be understood by taking the nickel.
Grimm, U; Grimm, Uwe; Schuetz, Gunter M.
1993-01-01
The finite-size scaling spectra of the spin-1/2 XXZ Heisenberg chain with toroidal boundary conditions and an even number of sites provide a projection mechanism yielding the spectra of models with a central charge c<1 including the unitary and non-unitary minimal series. Taking into account the half-integer angular momentum sectors - which correspond to chains with an odd number of sites - in many cases leads to new spinor operators appearing in the projected systems. These new sectors in the XXZ chain correspond to a new type of frustration lines in the projected minimal models. The corresponding new boundary conditions in the Hamiltonian limit are investigated for the Ising model and the 3-state Potts model and are shown to be related to duality transformations which are an additional symmetry at their self-dual critical point. By different ways of projecting systems we find models with the same central charge sharing the same operator content and modular invariant partition function which however diffe...
Institute of Scientific and Technical Information of China (English)
ZHANG Yong; LONG Gui-Lu; WU Yu-Chun; GUO Guang-Can
2007-01-01
Natural thermal entanglement between two qubits with ⅩⅩⅩ Heisenberg interaction is studied. For the antiferromagnet, increasing coupling strength or decreasing temperature under critical point increases the entanglement.Based on the thermal entanglement as quantum channel, entanglement and information of an input entangled state are transferred via partial teleportation. We find that the entanglement transferred will be lost during the process, and for the entanglement fidelity the partial teleportation is superior to classical communication as concurrence of entangled channel beyond 1/4. We show that both correlation information in input entangled state and individual information of the teleported particle are linearly dissipated. With more entanglement in quantum channel, more entanglement and correlation information can be transferred.
Institute of Scientific and Technical Information of China (English)
Xu Xiao-Bo; Liu Jin-Ming; Yu Peng-Fei
2008-01-01
Taking the intrinsic decoherence effect into account,this paper investigates the entanglement of a two-qubit anisotropic Heisenberg XY Z model in the presence of nonuniform external magnetic fields by employing the concurrence as entanglement measure.It is found that both the intrinsic decoherence and the anisotropy of the system give a significant suppression to the entanglement.Moreover it finds that the initial state of the system plays an important role in the time evolution of the entanglement,which means that the entanglement of the system is independent of the nonuniformity and uniformity of the magnetic field when the system is in the initial state |ψ(0)>=|00>and |ψ(0)>=m |01＞+n|10＞,respectively.
Approximation algorithms for two-state anti-ferromagnetic spin systems on bounded degree graphs
Sinclair, Alistair; Thurley, Marc
2011-01-01
In a seminal paper (Weitz, 2006), Weitz gave a deterministic fully polynomial approximation scheme for counting exponentially weighted independent sets (which is the same as approximating the partition function of the hard-core model from statistical physics) in graphs of degree at most d, up to the critical activity for the uniqueness of the Gibbs measure on the infinite d-regular tree. More recently Sly (see also Galanis et al, 2011) showed that this is optimal in the sense that if there is an FPRAS for the hard-core partition function on graphs of maximum degree d for activities larger than the critical activity on the infinite d-regular tree then NP = RP. In this paper we extend Weitz's approach to derive a deterministic fully polynomial approximation scheme for the partition function of general two-state anti-ferromagnetic spin systems on graphs of maximum degree d, up to the corresponding critical point on the d-regular tree. The main ingredient of our result is a proof that for two-state anti-ferromagn...
Energy Technology Data Exchange (ETDEWEB)
Wachter, Peter, E-mail: wachter@solid.phys.ethz.c [Laboratorium fuer Festkoerperphysik, ETH Zuerich, 8093 Zuerich (Switzerland)
2009-03-15
The new iron based high T{sub c} superconductors with T{sub c} up to 55 K have stirred new interest in this field. It is consensus that the BCS mechanism is not able to explain the high T{sub c}'s. In the following we propose that spin holes in anti-ferromagnetic clusters combine to make nonmagnetic bipolarons, which can condense and lead to superconductivity.
Liu, Guang-Hua; You, Wen-Long; Li, Wei; Su, Gang
2015-04-29
Quantum phase transitions (QPTs) and the ground-state phase diagram of the spin-1/2 Heisenberg-Ising alternating chain (HIAC) with uniform Dzyaloshinskii-Moriya (DM) interaction are investigated by a matrix-product-state (MPS) method. By calculating the odd- and even-string order parameters, we recognize two kinds of Haldane phases, i.e. the odd- and even-Haldane phases. Furthermore, doubly degenerate entanglement spectra on odd and even bonds are observed in odd- and even-Haldane phases, respectively. A rich phase diagram including four different phases, i.e. an antiferromagnetic (AF), AF stripe, odd- and even-Haldane phases, is obtained. These phases are found to be separated by continuous QPTs: the topological QPT between the odd- and even-Haldane phases is verified to be continuous and corresponds to conformal field theory with central charge c = 1; while the rest of the phase transitions in the phase diagram are found to be c = 1/2. We also revisit, with our MPS method, the exactly solvable case of HIAC model with DM interactions only on odd bonds and find that the even-Haldane phase disappears, but the other three phases, i.e. the AF, AF stripe and odd-Haldane phases, still remain in the phase diagram. We exhibit the evolution of the even-Haldane phase by tuning the DM interactions on the even bonds gradually.
Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13}: A new telluro-phosphate with S=1/2 Heisenberg chain
Energy Technology Data Exchange (ETDEWEB)
Xia, Mingjun [Beijing Center for Crystal Research and Development, Key Laboratory of Functional Crystals and Laser Technology, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190 (China); Shen, Shipeng; Lu, Jun; Sun, Young [Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Li, R.K., E-mail: rkli@mail.ipc.ac.cn [Beijing Center for Crystal Research and Development, Key Laboratory of Functional Crystals and Laser Technology, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190 (China)
2015-10-15
A new telluro-phosphate compound Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13} with S=1/2 Heisenberg chain has been successfully synthesized by solid state reaction and grown by flux method. Single crystal X-ray diffraction reveals that Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13} crystallizes into a monoclinic space group C2/c and cell parameters of a=17.647(3) Å, b=7.255(2) Å, c=9.191(2) Å and β=100.16 (3)°. In the structure of Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13}, one dimensional [CuTePO{sub 7}]{sup 3−} chains are formed by tetrahedral PO{sub 4} and trigonal bi-pyramidal TeO{sub 4} joining square planar CuO{sub 4} groups. Those [CuTePO{sub 7}]{sup 3−} chains are inter-connected by sharing one oxygen atom from the TeO{sub 4} group to form two dimensional layers. Magnetic susceptibility and specific heat measurements confirm that the title compound is a model one dimensional Heisenberg antiferromagnetic chain system. - Graphical abstract: Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13}, containing (CuTePO{sub 7}){sup 3−} chains formed by PO{sub 4} and TeO{sub 4} joining CuO{sub 4} groups, shows typical 1D Heisenberg antiferromagnetic chain model behavior as confirmed by magnetic measurements. - Highlights: • New telluro-phosphate Ba{sub 2}Cu{sub 2}Te{sub 2}P{sub 2}O{sub 13} has been grown. • It features layered structure composed of [CuTePO{sub 7}]{sup 3−} chains and TeO{sub 4} groups. • It shows the Heisenberg antiferromagnetic chain behavior. • It is transparent in the range of 1000–2500 nm with a UV absorption edge of 393 nm.
Energy Technology Data Exchange (ETDEWEB)
Rudowicz, Czesław, E-mail: crudowicz@zut.edu.pl
2014-03-01
Heisenberg antiferromagnetic chains based on Ni{sup 2+} ions with integer spin S=1 exhibit intriguing behavior, e.g. the Haldane gap phase and the large-D phase. The predicted transitions between the two phases and the Neel phase has generated search for real candidate systems. Crucial to this search is the interplay between the ‘in-plane anisotropy’, i.e. the rhombic zero-field splitting (ZFS) E-term, and the ‘planar anisotropy’, i.e. the axial ZFS D-term. This paper clarifies intricate properties of orthorhombic ZFS Hamiltonians (H{sub ZFS}) and inconsistencies revealed by critical survey of pertinent studies. Reporting the non-standard (D, E) sets with λ=E/D out of the standard range (0, 1/3) alongside the standard sets with λ∝(0, 1/3) indicates that these properties are not recognized. We show that direct comparisons of the non-standard and standard sets are meaningless and lead to incorrect conclusions on the strength of the ‘in-plane anisotropy’ (E) as compared with the ‘planar anisotropy’ (D). To remedy such problems, the ZFSP sets reported for the large-D phase candidate systems are reanalyzed using orthorhombic standardization. The six physically equivalent ZFSP sets are determined in the conventional (D, E) and Stevens (b{sub 2}{sup 0}, b{sub 2}{sup 2}) notation. These considerations help understanding intricacies inherent in orthorhombic H{sub ZFS} and provide consistent data for future modeling of ZFS parameters in the large-D phase and Haldane gap systems.
Energy Technology Data Exchange (ETDEWEB)
Barmettler, Peter; Gritsev, Vladimir [Department of Physics, University of Fribourg, CH-1700 Fribourg (Switzerland); Punk, Matthias [CPHT, Ecole Polytechnique, 91128 Palaiseau (France); Demler, Eugene [Department of Physics, Harvard University, Cambridge, MA 02138 (United States); Altman, Ehud, E-mail: peter.barmettler@cpht.polytechnique.f [Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100 (Israel)
2010-05-15
Recent experimental achievements in controlling ultracold gases in optical lattices open a new perspective on quantum many-body physics. In these experimental setups, it is possible to study coherent time evolution of isolated quantum systems. These dynamics reveal new physics beyond the low-energy properties that are usually relevant in solid-state many-body systems. In this paper, we study the time evolution of antiferromagnetic order in the Heisenberg chain after a sudden change of the anisotropy parameter, using various numerical and analytical methods. As a generic result, we find that the order parameter, which can show oscillatory or non-oscillatory dynamics, decays exponentially except for the effectively non-interacting case of the XX limit. For weakly ordered initial states, we also find evidence for an algebraic correction to the exponential law. The study is based on numerical simulations using a numerical matrix product method for infinite system sizes (iMPS), for which we provide a detailed description and an error analysis. Additionally, we investigate in detail the exactly solvable XX limit. These results are compared to approximative analytical approaches including an effective description by the XZ model as well as by mean-field, Luttinger-liquid and sine-Gordon theories. The comparison reveals which aspects of non-equilibrium dynamics can, as in equilibrium, be described by low-energy theories and which are the novel phenomena specific to quantum quench dynamics. The relevance of the energetically high part of the spectrum is illustrated by means of a full numerical diagonalization of the Hamiltonian.
Tang, Bing; Li, Guang-Ling; Fu, Mei
2017-03-01
A semiclassical theoretical study on the property of the modulational instability of corresponding linear spin-waves and the presence of nonlinear localized excitations in a discrete quantum ferromagnetic spin chain with single-ion easy-axis anisotropy is reported. We consider the Glauber coherent-state representation combined with the Dyson-Maleev transformation for local spin operators as the basic representation of the system, and derive the equation of motion by means of the Ehrenfest theorem. Using a modulational instability analysis of plane waves, we predict the existence regions of bright envelope solitons and intrinsic localized spin-wave modes. Besides, with the help of a semidiscrete multi-scale method, we obtain analytical solutions for the bright envelope soliton and intrinsic localized spin-wave mode. Moreover, we analyze their existence conditions, which agree with the results of modulational instability analysis.
Brackett, Jeremy; Newman, Joseph; De Silva, Theja N.
2016-10-01
We study an effective fermion model on a square lattice to investigate the cooperation and competition of superconductivity and anti-ferromagnetism. In addition to particle tunneling and on-site interaction, a bosonic excitation mediated attractive interaction is also included in the model. We assume that the attractive interaction is mediated by spin fluctuations and excitations of Bose-Einstein condensation (BEC) in electronic systems and Bose-Fermi mixtures on optical lattices, respectively. Using an effective mean-field theory to treat both superconductivity and anti-ferromagnetism at equal footing, we study a single effective model relevant for both systems within the Landau energy functional approach and a linearized theory. Within our approaches, we find possible co-existence of superconductivity and anti-ferromagnetism for both electronic and cold-atomic models. Our linearized theory shows while spin fluctuations favor d-wave superconductivity and BEC excitations favor s-wave superconductivity.
Cassidy, David C.
1978-01-01
Describes some of the discussion, correspondances and assumptions of Heisenberg. Includes clarifying and defending his explanation of the anomalous Zeeman Effect to the Quantum Physicists of his time. (GA)
Heisenberg's wave packet reconsidered
Grabbe, J. Orlin
2005-01-01
This note shows that Heisenberg's choice for a wave function in his original paper on the uncertainty principle is simply a renormalized characteristic function of a stable distribution with certain restrictions on the parameters. Relaxing Heisenberg's restrictions leads to a more general formulation of the uncertainty principle. This reformulation shows quantum uncertainty can exist at a macroscopic level. These modifications also give rise to a new form of Schrodinger's wave equation as the...
Rotational Heisenberg Inequalities
Bréchet, Sylvain; Reuse, François; Maschke, Klaus; Ansermet, Jean-Philippe
2015-01-01
Since their discovery in 1927, the Heisenberg Inequalities have become an icon of quantum mechanics. Often inappropriately referred to as the Uncertainty Principle, these inequalities relating the standard deviations of the position and momentum observables to Planck's constant are one of the cornerstones of the quantum formalism even if the physical interpretation of quantum mechanics remains still open to controversy nowadays. The Heisenberg Inequalities governing translational motion are w...
Heisenberg's observability principle
Wolff, JE
2014-01-01
Werner Heisenberg's 1925 paper ‘Quantum-theoretical re-interpretation of kinematic and mechanical relations’ marks the beginning of quantum mechanics. Heisenberg famously claims that the paper is based on the idea that the new quantum mechanics should be ‘founded exclusively upon relationships between quantities which in principle are observable’. My paper is an attempt to understand this observability principle, and to see whether its employment is philosophically defensible. Against interpr...
The replica symmetric solution for orthogonally constrained Heisenberg model on Bethe lattice
Concetti, Francesco
2017-02-01
In this paper, we study the thermodynamic properties of a system of D-components classical Heisenberg spins lying on the vertices of a random regular graph, with an unconventional first neighbor non-random interaction J{{≤ft({{\\mathbf{S}}i}\\centerdot {{\\mathbf{S}}k}\\right)}2} . We can consider this model as a continuum version of anti-ferromagnetic D-states Potts model. We compute the paramagnetic free energy, using a new approach, presented in this paper for the first time, based on the replica method. Through the linear stability analysis, we obtain an instability line on the temperature-connectivity plane that provides a bound to the appearance of a phase transition. We also argue about the character of the instability observed.
Energy Technology Data Exchange (ETDEWEB)
Matsushita, M., E-mail: matsushita@eng.ehime-u.ac.j [Department of Mechanical Engineering, Graduate School of Science and Engineering, Ehime University, 3-Bunkyocho, Matsuyama 790-0826 (Japan); Nakano, S. [National Institute for Materials Science, Tsukuba, Ibaraki 305-0044 (Japan); Ohfuji, H. [Geodynamics Research Center, Ehime University, 2-Bunkyocho, Matsuyama 790-0826 (Japan); Yamada, I. [Department of Chemistry and Biology, Graduate School of Science and Engineering, Ehime University, 2-Bunkyocho, Matsuyama 790-0826 (Japan); Kikegawa, T. [High Energy Accelerator Research Organization, Tsukuba 305-0801 (Japan)
2011-03-15
We have investigated the pressure variation of the volume and structure of an FCC Fe{sub 64}Mn{sub 36} anti-ferromagnetic Invar alloy. The inclination of the pressure-volume (P-V) curve of the FCC structure becomes discontinuous at a pressure of 4 GPa. According to the bulk modulus at zero pressure estimated by the Birch-Murnaghan equation of state, the pressure between 4 and 10 GPa is 33 GPa larger than that at a pressure below 4 GPa. Considering previous experiments on magnetism at high pressure the Neel temperature at 4 GPa almost decreases to room temperature. These results suggest that the increase in the bulk modulus by 33 GPa can be attributed to the pressure-induced magnetic phase transition from anti-ferromagnetism to paramagnetism. Volume at zero pressure was estimated using the Birch-Murnaghan equation of state. The volume of FCC structure in the anti-ferromagnetic state was 1.17% larger than the volume in the paramagnetic state, namely, the spontaneous magnetostriction was 1.17%. Pressure-induced structural transition from FCC to HCP occurs with an increase in the pressure, especially at up to 5 GPa. The value of c/a is 1.62; this value almost corresponds to that of an ideal HCP structure. The bulk modulus of the HCP structure estimated by the Birch-Murnaghan equation of state is larger than that of the FCC structure, and the volume/atom ratio is smaller than that of the FCC structure. - Research highlights: > We have investigated the pressure variation of volume and structure of FCC Fe{sub 64}Mn{sub 36} alloy. > We discovered that the change in inclination of the pressure-volume (P-V) curve of the FCC structure becomes discontinuous at a pressure of 4 GPa. This pressure corresponds to the Neel temperature, which decreases down to room temperature. > Further we estimated bulk modulus and volume at zero pressure using the Birch-Murnaghan equation of state. As a result, we have demonstrated that anti-ferromagnetism has very close relationship with the
Impurity modes in the one-dimensional XXZ Heisenberg model
Energy Technology Data Exchange (ETDEWEB)
Sousa, J.M. [Departamento de Física, Universidade Federal do Piauí, Campus Ministro Petrônio Portella, 57072-970 Teresina, Piauí (Brazil); Leite, R.V. [Centro de Ciências Exatas e Tecnologia, Curso de Física, Universidade Estadual Vale do Acaraú, Av. Dr. Guarany 317, Campus Cidao, 62040-730 Sobral, Ceará (Brazil); Landim, R.R. [Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, Ceará (Brazil); Costa Filho, R.N., E-mail: rai@fisica.ufc.br [Departamento de Física, Universidade Federal do Ceará, Caixa Postal 6030, Campus do Pici, 60455-760 Fortaleza, Ceará (Brazil)
2014-04-01
A Green's function formalism is used to calculate the energy of impurity modes associated with one and/or two magnetic impurities in the one-dimensional Heisenberg XXZ magnetic chain. The system can be tuned from the Heisenberg to the Ising model varying a parameter λ. A numerical study is performed showing two types of localized modes (s and p). The modes depend on λ and the degeneracy of the acoustic modes is broken.
HEISENBERG'S INEQUALITY AND LOGARITHMIC HEISENBERG'S INEQUALITY FOR AMBIGUITY FUNCTION
Institute of Scientific and Technical Information of China (English)
Tian Guji
2000-01-01
In this article we discuss the relation between Heisenberg's inequality and logarithmic Heisenberg's (entropy) inequality for ambiguity function. After building up a Heisenberg's inequality, we obtain a connection of variance with entropy by variational method. Using classical Taylor's expansion, we prove that the equality in Heisenberg's inequality holds if and only if the entropy of 2k - 1 order is equal to (2k - 1)!.
S=5/2 spin-chain Heisenberg systems SrMn{sub 2}V{sub 2}O{sub 8} and BaMn{sub 2}V{sub 2}O{sub 8}
Energy Technology Data Exchange (ETDEWEB)
Niesen, Sandra; Kolland, Gerhard; Heyer, Oliver; Valldor, Martin; Lorenz, Thomas [II. Physikalisches Institut, Universitaet Koeln (Germany)
2012-07-01
Low-dimensional magnetic systems are commonly studied due to their interesting magnetic properties. For small spin values (S=1/2 or 1), the groundstate and the low-lying excitations are often dominated by strong quantum fluctuations, while a more classical behavior is expected for systems with larger spins. In this context, the series AM{sub 2}X{sub 2}O{sub 8} (A=Ba,Sr,Pb; M=Cu,Co,Ni,Mn; X=V,As) are of particular interest. Depending on the transition metal, different spins are realized and the structure contains screw chains of octahedrally coordinated M{sup 2+} ions along the c axis of the tetragonal structure. These chains are spatially separated by a nonmagnetic matrix, resulting in a quasi-1D magnetic system. The Heisenberg S=5/2 system BaMn{sub 2}V{sub 2}O{sub 8} shows low-dimensional behavior with a broad maximum of {chi}(T) around 170 K but finally orders antiferromagnetically at 37 K. Up to now only few studies of polycristalline BaMn{sub 2}V{sub 2}O{sub 8} were available. Large single crystals of BaMn{sub 2}V{sub 2}O{sub 8} and of the new compound SrMn{sub 2}V{sub 2}O{sub 8} were prepared. The crystal structure and the basic physical properties of this new compound are presented.
Energy Technology Data Exchange (ETDEWEB)
Wang, Pan [State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China); School of Science, Beijing University of Posts and Telecommunications, P.O. Box 122, Beijing 100876 (China); Tian, Bo, E-mail: tian.bupt@yahoo.com.cn [State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China); School of Science, Beijing University of Posts and Telecommunications, P.O. Box 122, Beijing 100876 (China); Jiang, Yan; Wang, Yu-Feng [State Key Laboratory of Information Photonics and Optical Communications, Beijing University of Posts and Telecommunications, Beijing 100876 (China); School of Science, Beijing University of Posts and Telecommunications, P.O. Box 122, Beijing 100876 (China)
2013-02-15
For describing the dynamics of alpha helical proteins with internal molecular excitations, nonlinear couplings between lattice vibrations and molecular excitations, and spin excitations in one-dimensional isotropic biquadratic Heisenberg ferromagnetic spin with the octupole–dipole interactions, we consider an inhomogeneous generalized fourth-order nonlinear Schrödinger equation. Based on the Ablowitz–Kaup–Newell–Segur system, infinitely many conservation laws for the equation are derived. Through the auxiliary function, bilinear forms and N-soliton solutions for the equation are obtained. Interactions of solitons are discussed by means of the asymptotic analysis. Effects of linear inhomogeneity on the interactions of solitons are also investigated graphically and analytically. Since the inhomogeneous coefficient of the equation h=α x+β, the soliton takes on the parabolic profile during the evolution. Soliton velocity is related to the parameter α, distance scale coefficient and biquadratic exchange coefficient, but has no relation with the parameter β. Soliton amplitude and width are only related to α. Soliton position is related to β.
Heisenberg necklace model in a magnetic field
Tsvelik, A. M.; Zaliznyak, I. A.
2016-08-01
We study the low-energy sector of the Heisenberg necklace model. Using the field-theory methods, we estimate how the coupling of the electronic spins with the paramagnetic Kondo spins affects the overall spin dynamics and evaluate its dependence on a magnetic field. We are motivated by the experimental realizations of the spin-1/2 Heisenberg chains in SrCuO2 and Sr2CuO3 cuprates, which remain one-dimensional Luttinger liquids down to temperatures much lower than the in-chain exchange coupling J . We consider the perturbation of the energy spectrum caused by the interaction γ with nuclear spins (I =3 /2 ) present on the same sites. We find that the resulting necklace model has a characteristic energy scale, Λ ˜J1 /3(γI ) 2 /3 , at which the coupling between (nuclear) spins of the necklace and the spins of the Heisenberg chain becomes strong. This energy scale is insensitive to a magnetic field B . For μBB >Λ we find two gapless bosonic modes that have different velocities, whose ratio at strong fields approaches a universal number, √{2 }+1 .
Spatially anisotropic Heisenberg kagome antiferromagnet
Apel, W.; Yavors'kii, T.; Everts, H.-U.
2007-04-01
In the search for spin-1/2 kagome antiferromagnets, the mineral volborthite has recently been the subject of experimental studies (Hiroi et al 2001 J. Phys. Soc. Japan 70 3377; Fukaya et al 2003 Phys. Rev. Lett. 91 207603; Bert et al 2004 J. Phys.: Condens. Matter 16 S829; Bert et al 2005 Phys. Rev. Lett. 95 087203). It has been suggested that the magnetic properties of this material are described by a spin-1/2 Heisenberg model on the kagome lattice with spatially anisotropic exchange couplings. We report on investigations of the {\\mathrm {Sp}}(\\mathcal {N}) symmetric generalization of this model in the large \\mathcal {N} limit. We obtain a detailed description of the dependence of possible ground states on the anisotropy and on the spin length S. A fairly rich phase diagram with a ferrimagnetic phase, incommensurate phases with and without long-range order and a decoupled chain phase emerges.
Energy Technology Data Exchange (ETDEWEB)
Wang, Guangmei [Ruhr-Universitat Bochum; Valldor, Martin [Max Plank Institute for Chemical Physics of Solids, Dresden, Germany; Mallick, Bert [Ruhr Universitat Bochum; Mudring, Anja-Verena [Ames Laboratory
2014-01-01
Four open-framework transition-metal phosphates; (NH4)2Co3(HPO4)2F4 (1), (NH4)Co3(HPO4)2(H2PO4)F2 (2), KCo3(HPO4)2(H2PO4)F2 (3), and KFe3(HPO4)2(H2PO4)F2 (4); are prepared by ionothermal synthesis using pyridinium hexafluorophosphate as the ionic liquid. Single-crystal X-ray diffraction analyses reveal that the four compounds contain cobalt/iron–oxygen/fluoride layers with Kagomé topology composed of interlinked face-sharing MO3F3/MO4F2 octahedra. PO3OH pseudo-tetrahedral groups augment the [M3O6F4] (1)/[M3O8F2] layers on both sides to give M3(HPO4)2F4 (1) and M3(HPO4)2F2 (2–4) layers. These layers are stacked along the a axis in a sequence AA…, resulting in the formation of a layer structure for (NH4)2Co3(HPO4)2F4(1). In NH4Co3(HPO4)2(H2PO4)F2 and KM3(HPO4)2(H2PO4)F2, the M3(HPO4)2F2 layers are stacked along the a axis in a sequence AAi… and are connected by [PO3(OH)] tetrahedra, giving rise to a 3-D open framework structure with 10-ring channels along the [001] direction. The negative charges of the inorganic framework are balanced by K+/NH4+ ions located within the channels. The magnetic transition metal cations themselves form layers with stair-case Kagomé topology. Magnetic susceptibility and magnetization measurements reveal that all four compounds exhibit a canted anti-ferromagnetic ground state (Tc = 10 or 13 K for Co and Tc = 27 K for Fe) with different canting angles. The full orbital moment is observed for both Co2+ and Fe2+.
Energy Technology Data Exchange (ETDEWEB)
Yang, Jin-Wei; Gao, Yi-Tian, E-mail: gaoyt163@163.com; Wang, Qi-Min; Su, Chuan-Qi; Feng, Yu-Jie; Yu, Xin
2016-01-15
In this paper, a fourth-order variable-coefficient nonlinear Schrödinger equation is studied, which might describe a one-dimensional continuum anisotropic Heisenberg ferromagnetic spin chain with the octuple–dipole interaction or an alpha helical protein with higher-order excitations and interactions under continuum approximation. With the aid of auxiliary function, we derive the bilinear forms and corresponding constraints on the variable coefficients. Via the symbolic computation, we obtain the Lax pair, infinitely many conservation laws, one-, two- and three-soliton solutions. We discuss the influence of the variable coefficients on the solitons. With different choices of the variable coefficients, we obtain the parabolic, cubic, and periodic solitons, respectively. We analyse the head-on and overtaking interactions between/among the two and three solitons. Interactions between a bound state and a single soliton are displayed with different choices of variable coefficients. We also derive the quasi-periodic formulae for the three cases of the bound states.
Gradings and Symmetries on Heisenberg type algebras
A. Calderón; C. Draper; Martín, C.; Sánchez, T.
2014-01-01
We describe the fine (group) gradings on the Heisenberg algebras, on the Heisenberg superalgebras and on the twisted Heisenberg algebras. We compute the Weyl groups of these gradings. Also the results obtained respect to Heisenberg superalgebras are applied to the study of Heisenberg Lie color algebras.
Deguchi, Tetsuo; Ranjan Giri, Pulak
2016-04-01
Every solution of the Bethe-ansatz equations (BAEs) is characterized by a set of quantum numbers, by which we can evaluate it numerically. However, no general rule is known how to give quantum numbers for the physical solutions of BAE. For the spin-1/2 XXX chain we rigorously derive all the quantum numbers for the complete set of the Bethe-ansatz eigenvectors in the two down-spin sector with any chain length N. Here we obtain them both for real and complex solutions. We also show that all the solutions associated with them are distinct. Consequently, we prove the completeness of the Bethe ansatz and give an exact expression for the number of real solutions which correspond to collapsed bound-state solutions (i.e., two-string solutions) in the sector: 2[(N-1)/2-(N/π ){{tan}}-1(\\sqrt{N-1})] in terms of Gauss’ symbol. Moreover, we prove in the sector the scheme conjectured by Takahashi for solving BAE systematically. We also suggest that by applying the present method we can derive the quantum numbers for the spin-1/2 XXZ chain.
Generalised Heisenberg Relations
Brody, Dorje C.; Hughston, Lane P.
1997-01-01
A geometric framework for quantum statistical estimation is used to establish a series of higher order corrections to the Heisenberg uncertainty relations associated with pairs of canonically conjugate variables. These corrections can be expressed in terms of linear combinations of higher order cumulants for the distributions, and thus vanish for Gaussian distributions. Estimates for typical numerical values arising from these corrections are indicated in the case of a gamma distribution.
Heisenberg's uncertainty principle
Busch, Paul; Heinonen, Teiko; Lahti, Pekka
2007-01-01
Heisenberg's uncertainty principle is usually taken to express a limitation of operational possibilities imposed by quantum mechanics. Here we demonstrate that the full content of this principle also includes its positive role as a condition ensuring that mutually exclusive experimental options can be reconciled if an appropriate trade-off is accepted. The uncertainty principle is shown to appear in three manifestations, in the form of uncertainty relations: for the widths of the position and...
HEISENBERG'S INEQUALITY IN SOBOLEV SPACES
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Using the correspondence between psedodifferential operator and its symbol,the authors obtain Heisenberg's inequality in Sobolev spaces and therefore a kind of quantitative representation of uncertainty principle.
Directory of Open Access Journals (Sweden)
Xin Yan
2015-07-01
Full Text Available The Schwinger-boson mean-field theory (SBMFT and the linearized tensor renormalization group (LTRG methods are complementarily applied to explore the thermodynamics of the quantum ferromagnetic mixed spin (S, σ chains. It is found that the system has double excitations, i.e. a gapless and a gapped excitation; the low-lying spectrum can be approximated by ω k ∼ S σ 2 ( S + σ J k 2 with J the ferromagnetic coupling; and the gap between the two branches is estimated to be △ ∼ J. The Bose-Einstein condensation indicates a ferromagnetic ground state with magnetization m tot z = N ( S + σ . At low temperature, the spin correlation length is inversely proportional to temperature (T, the susceptibility behaviors as χ = a 1 ∗ 1 T 2 + a 2 ∗ 1 T , and the specific heat has the form of C = c 1 ∗ T − c 2 ∗ T + c 3 ∗ T 3 2 , with ai (i = 1, 2 and ci (i = 1, 2, 3 the temperature independent constants. The SBMFT results are shown to be in qualitatively agreement with those by the LTRG numerical calculations for S = 1 and σ = 1/2. A comparison of the LTRG results with the experimental data of the model material MnIINiII(NO24(en2(en = ethylenediamine, is made, in which the coupling parameters of the compound are obtained. This study provides useful information for deeply understanding the physical properties of quantum ferromagnetic mixed spin chain materials.
Determinant representations for correlation functions of spin-1/2 Heisenberg XXZ magnets
Essler, F H L; Izergin, A G; Korepin, V E
1994-01-01
We consider correlation functions of the spin-\\half XXX and XXZ Heisenberg chains in a magnetic field. Starting from the algebraic Bethe Ansatz we derive representations for various correlation functions in terms of determinants of Fredholm integral operators.
Quantum Heisenberg--Weyl Algebras
Ballesteros, Angel; Herranz, Francisco J.; Parashar, Preeti
1996-01-01
All Lie bialgebra structures on the Heisenberg--Weyl algebra $[A_+,A_-]=M$ are classified and explicitly quantized. The complete list of quantum Heisenberg--Weyl algebras so obtained includes new multiparameter deformations, most of them being of the non-coboundary type.
Simulation of time-dependent Heisenberg models in one dimension
DEFF Research Database (Denmark)
Volosniev, A. G.; Hammer, H. -W.; Zinner, N. T.
2016-01-01
In this Letter, we provide a theoretical analysis of strongly interacting quantum systems confined by a time-dependent external potential in one spatial dimension. We show that such systems can be used to simulate spin chains described by Heisenberg Hamiltonians in which the exchange coupling...
Gapless chiral spin liquid in a kagome Heisenberg model
Bieri, Samuel; Messio, Laura; Bernu, Bernard; Lhuillier, Claire
2015-08-01
Motivated by recent experiments on the Heisenberg S =1 /2 quantum spin liquid candidate material kapellasite, we classify all possible chiral (time-reversal symmetry breaking) spin liquids with fermionic spinons on the kagome lattice. We obtain the phase diagram for the physically relevant extended Heisenberg model, comparing the energies of a wide range of microscopic variational wave functions. We propose that, at low temperature, kapellasite exhibits a gapless chiral spin liquid phase with spinon Fermi surfaces. This two-dimensional state inherits many properties of the nearby one-dimensional phase of decoupled antiferromagnetic spin chains, but also shows some remarkable differences. We discuss the spin structure factors and other physical properties.
Type-I integrable quantum impurities in the Heisenberg model
Doikou, Anastasia
2013-01-01
Type-I quantum impurities are investigated in the context of the integrable Heisenberg model. This type of defects is associated to the (q)-harmonic oscillator algebra. The transmission matrices associated to this particular type of defects are computed via the Bethe ansatz methodology for the XXX model, as well as for the critical and non-critical XXZ spin chain. In the attractive regime of the critical XXZ spin chain the transmission amplitudes for the breathers are also identified.
Type-I integrable quantum impurities in the Heisenberg model
Energy Technology Data Exchange (ETDEWEB)
Doikou, Anastasia, E-mail: adoikou@upatras.gr
2013-12-21
Type-I quantum impurities are investigated in the context of the integrable Heisenberg model. This type of defects is associated to the (q)-harmonic oscillator algebra. The transmission matrices associated to this particular type of defects are computed via the Bethe ansatz methodology for the XXX model, as well as for the critical and non-critical XXZ spin chain. In the attractive regime of the critical XXZ spin chain the transmission amplitudes for the breathers are also identified.
Directory of Open Access Journals (Sweden)
Ynduráin, Francisco J.
2002-01-01
Full Text Available Not available
Los azares de las onomásticas hacen coincidir en este año el centenario del nacimiento de tres de los más grandes físicos del siglo XX. Dos de ellos, Fermi y Heisenberg, dejaron una marca fundamental en la ciencia (ambos, pero sobre todo el segundo y, el primero, también en la tecnología. Lawrence, indudablemente de un nivel inferior al de los otros dos, estuvo sin embargo en el origen de uno de los desarrollos tecnológicos que han sido básicos para la exploración del universo subnuclear en la segunda mitad del siglo que ha terminado hace poco, el de los aceleradores de partículas.
Heisenberg symmetry and hypermultiplet manifolds
Antoniadis, Ignatios; Petropoulos, P Marios; Siampos, Konstantinos
2015-01-01
We study the emergence of Heisenberg (Bianchi II) algebra in hyper-K\\"ahler and quaternionic spaces. This is motivated by the r\\^ole these spaces with this symmetry play in $\\mathcal{N}=2$ hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-K\\"ahler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing cosmological constant. We further apply this method for the two hyper-K\\"ahler spaces with Heisenberg algebra, which is reduced to $U(1)\\times U(1)$ at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry -- as opposed to $\\text{Heisenberg} \\ltimes U(1)$. We finally discuss the realization of the latter by gauging appropriate $Sp(2,4)$ generators in $\\mathcal{N}=2$ conformal supergravity.
Directory of Open Access Journals (Sweden)
Z. Wu
2014-04-01
Full Text Available In this manuscript, we describe how the map of high frequency conductivity distribution of an oxide-doped anti-ferromagnetic 200 nm thin film can be obtained from the quality factor (Q measured by a near-field scanning microwave microscope (NSMM. Finite element analysis (FEA is employed to simulate the NSMM tip-sample interaction and obtain a curve related between the simulated quality factor (Q and conductivity. The curve is calibrated by a standard Cu thin film with thickness of 200 nm, together with NSMM measured Q of Ag, Au, Fe, Cr and Ti thin films. The experimental conductivity obtained by the NSMM for IrMn thin films with various doped concentrations of Al2O3 is found consistent with conventional voltammetry measurement in the same tendency. That conductivity decreases as the content of doped Al2O3 increases. The results and images obtained demonstrate that NSMM can be employed in thin film analysis for characterization of local electrical properties of materials in a non-destructive manner and for obtaining a map of conductivity distribution on the same film.
Thermal effects on quantum communication through spin chains
Bayat, A; Bayat, Abolfazl; Karimipour, Vahid
2004-01-01
We study the effect of thermal fluctuations in a recently proposed protocol for transmission of unknown quantum states through quantum spin chains. We develop a low temperature expansion for general spin chains. We then apply this formalism to study exactly thermal effects on short spin chains of four spins. We show that optimal times for extraction of output states are almost independent of the temperature which lowers only the fidelity of the channel. Moreover we show that thermal effects are smaller in the anti-ferromagnetic chains than the ferromagnetic ones.
Cohomology of Heisenberg Lie superalgebras
Bai, Wei; Liu, Wende
2017-02-01
Suppose the ground field to be algebraically closed and of characteristic different from 2 and 3. All Heisenberg Lie superalgebras consist of two super-versions of the Heisenberg Lie algebras, 𝔥2m,n and 𝔟𝔞n with m a non-negative integer and n a positive integer. The space of a "classical" Heisenberg Lie superalgebra 𝔥2m,n is the direct sum of a superspace with a non-degenerate anti-supersymmetric even bilinear form and a one-dimensional space of values of this form constituting the even center. The other super-analog of the Heisenberg Lie algebra, 𝔟𝔞n, is constructed by means of a non-degenerate anti-supersymmetric odd bilinear form with values in the one-dimensional odd center. In this paper, we study the cohomology of 𝔥2m,n and 𝔟𝔞n with coefficients in the trivial module by using the Hochschild-Serre spectral sequences relative to a suitable ideal. In the characteristic zero case, for any Heisenberg Lie superalgebra, we determine completely the Betti numbers and associative superalgebra structures for their cohomology. In the characteristic p > 3 case, we determine the associative superalgebra structure for the divided power cohomology of 𝔟𝔞n and we also make an attempt to determine the divided power cohomology of 𝔥2m,n by computing it in a low-dimensional case.
Berry phase in Heisenberg representation
Andreev, V. A.; Klimov, Andrei B.; Lerner, Peter B.
1994-01-01
We define the Berry phase for the Heisenberg operators. This definition is motivated by the calculation of the phase shifts by different techniques. These techniques are: the solution of the Heisenberg equations of motion, the solution of the Schrodinger equation in coherent-state representation, and the direct computation of the evolution operator. Our definition of the Berry phase in the Heisenberg representation is consistent with the underlying supersymmetry of the model in the following sense. The structural blocks of the Hamiltonians of supersymmetrical quantum mechanics ('superpairs') are connected by transformations which conserve the similarity in structure of the energy levels of superpairs. These transformations include transformation of phase of the creation-annihilation operators, which are generated by adiabatic cyclic evolution of the parameters of the system.
Cosmological implications of Heisenberg's principle
Gonzalo, Julio A
2015-01-01
The aim of this book is to analyze the all important implications of Heisenberg's Uncertainty Principle for a finite universe with very large mass-energy content such as ours. The earlier and main contributors to the formulation of Quantum Mechanics are briefly reviewed regarding the formulation of Heisenberg's Principle. After discussing “indeterminacy” versus ”uncertainty”, the universal constants of physics are reviewed and Planck's units are given. Next, a novel set of units, Heisenberg–Lemaitre units, are defined in terms of the large finite mass of the universe. With the help of Heisenberg's principle, the time evolution of the finite zero-point energy for the universe is investigated quantitatively. Next, taking advantage of the rigorous solutions of Einstein's cosmological equation for a flat, open and mixed universe of finite mass, the most recent and accurate data on the “age” (to) and the expansion rate (Ho) of the universe and their implications are reconsidered.
Heisenberg symmetry and hypermultiplet manifolds
Directory of Open Access Journals (Sweden)
Ignatios Antoniadis
2016-04-01
Full Text Available We study the emergence of Heisenberg (Bianchi II algebra in hyper-Kähler and quaternionic spaces. This is motivated by the rôle these spaces with this symmetry play in N=2 hypermultiplet scalar manifolds. We show how to construct related pairs of hyper-Kähler and quaternionic spaces under general symmetry assumptions, the former being a zooming-in limit of the latter at vanishing scalar curvature. We further apply this method for the two hyper-Kähler spaces with Heisenberg algebra, which is reduced to U(1×U(1 at the quaternionic level. We also show that no quaternionic spaces exist with a strict Heisenberg symmetry – as opposed to Heisenberg⋉U(1. We finally discuss the realization of the latter by gauging appropriate Sp(2,4 generators in N=2 conformal supergravity.
Quasisymmetric functions and Heisenberg doubles
Directory of Open Access Journals (Sweden)
Jie Sun
2016-09-01
Full Text Available The ring of quasisymmetric functions is free over the ring of symmetric functions. This result waspreviously proved by M. Hazewinkel combinatorially through constructing a polynomial basis forquasisymmetric functions. The recent work by A. Savage and O. Yacobi on representation theoryprovides a new proof to this result. In this paper, we proved that under certain conditions, thepositive part of a Heisenberg double is free over the positive part of the corresponding projectiveHeisenberg double. Examples satisfying the above conditions are discussed.
Heisenberg model and Rigged Configurations
Giri, Pulak Ranjan
2015-01-01
We show a correspondence of all the solutions of the spin-1/2 isotropic Heisenberg model for N=12 to the rigged configurations based on the comparison of the set of Takahashi quantum numbers in lexicographical order with the set of riggings of the rigged configurations in co-lexicographical order.
Todorov, Ivan
2005-01-01
A brief review of Heisenberg's life and work: participating in the youth movement in the aftermath of World War I, creating quantum mechanics, conflict with "deutsche Physik", involvement in "Hitler's Uranium Project", last illusions. Problems and dilemmas for scientists under a dictatorship - East and West.
Werner Heisenberg - Life and Work
2002-01-01
Werner Heisenberg (centre) with Wolfgang Pauli (left) and Enrico Fermi on Lake Como, September 1927. An exhibition on the life and work of Werner Heisenberg will be on display in the Main Building (Mezzanine) at CERN from 1 - 23 July. The exhibition was produced by the University Archive of Leipzig University (Gerald Wiemers) and the Max-Planck-Institut für Physik in Munich (Helmut Rechenberg) to mark the centenary of Heisenberg's birth in 1901. German theoretical physicist Werner Karl Heisenberg (5 December 1901 - 1 February 1976) was one of the leading scientists of the 20th century. He carried out important work in nuclear and particle physics, but his most significant contribution was to the development of quantum mechanics. He is best known for his uncertainty principle, which restricts the accuracy with which some properties of atoms and particles - such as position and linear momentum - can be determined simultaneously. In 1932 he was awarded the Noble Prize in Physics 'for the creation of q...
Werner Heisenberg - Life and Work
2002-01-01
Werner Heisenberg (centre) with Wolfgang Pauli and Enrico Fermi, 1927. An exhibition on the life and work of Werner Heisenberg will be on display in the Main Building (Mezzanine) at CERN from 1 - 30 July*. German theoretical physicist Werner Karl Heisenberg (1901 - 1976) was one of the leading scientists of the 20th century. Nobel Prize in Physics in 1932, his most significant contribution was to the development of quantum mechanics. He is best known for his uncertainty principle, which restricts the accuracy with which some properties of atoms and particles can be determined simultaneously. Heisenberg was a keen supporter of CERN, and was as the first chairman of CERN's Scientific Policy Committee in October 1954. A related celebration will take place in the TH Amphitheatre (4/3-006), on Thursday 18 July at 16:00. After an introduction from the Director-General Luciano Maiani, his daughter, Barbara Blum, his last postgraduate, Helmut Rechenberg and Valentin Telegdi will evoke memories of the life and work ...
Institute of Scientific and Technical Information of China (English)
刘芬芬; 梁承红; 张勇; 邢红宏
2012-01-01
The coexistence of anti-ferromagnetism and superconductivity of superconductors were investigated in a renormalized mean field theory based on the Gutzwiller variational approach in the two dimensions hole-doped t-t'-J -U model. The effects on the coexistence were discussed. The anti-ferromagnetic order coexists with the d-wave superconductivity in the under doped region below the doping δ≤0. 1. The anti - ferromagnetism orders are greatly enhanced with the increasing of the next-nearest-neighbor hopping (t'). The superconductivity order are slightly suppressed by t' in under doped regions and enhanced in over doped, so the coexistence extends to the larger one. The ground state energy of the coexistent state is always lower than that of the pure superconductivity state.%在二维空穴掺杂t-t′-J-U模型和重整化平均场理论的框架下,用Gutzwiller方法研究了Gossamer超导体的超导电性和反铁磁性的共存,探讨了电子次近邻跃迁对共存的影响,发现在掺杂浓度δ≤0.1的欠掺杂区反铁磁序和超导序共存.随着电子次近邻跃迁的增大,反铁磁序得到增强,超导序参数在欠掺杂区域受到抑制,在过掺杂区明显地得到增强,导致反铁磁序和超导序共存区域变大.超导序和反铁磁序共存的状态比纯粹的超导态能量低,共存状态更稳定.
Dielectric relaxation and anti-ferromagnetic coupling of BiEuO{sub 3} and BiGdO{sub 3}
Energy Technology Data Exchange (ETDEWEB)
Saha, Sujoy, E-mail: sahasujoy3@gmail.com [Department of Physics, Bose Institute, 93/1 Acharya Prafulla Chandra Road, Kolkata 700009 (India); Chanda, Sadhan; Dutta, Alo [Department of Physics, Bose Institute, 93/1 Acharya Prafulla Chandra Road, Kolkata 700009 (India); Kumar, Uday [Department of Physical Sciences, Indian Institute of Science Education and Research, Kolkata, Mohanpur 741252 (India); Ranjan, Rajeev [Department of Materials Engineering, Indian Institute of Science, Bangalore 560012 (India); Sinha, T.P. [Department of Physics, Bose Institute, 93/1 Acharya Prafulla Chandra Road, Kolkata 700009 (India)
2014-06-01
BiEuO{sub 3} (BE) and BiGdO{sub 3} (BG) are synthesized by the solid-state reaction technique. Rietveld refinement of the X-ray diffraction data shows that the samples are crystallized in cubic phase at room temperature having Fm3m symmetry with the lattice parameters of 5.4925(2) and 5.4712(2) Å for BE and BG, respectively. Raman spectra of the samples are investigated to obtain the phonon modes of the samples. The dielectric properties of the samples are investigated in the frequency range from 42 Hz to 1.1 MHz and in the temperature range from 303 K to 673 K. An analysis of the real and imaginary parts of impedance is performed assuming a distribution of relaxation times as confirmed by the Cole–Cole plots. The frequency-dependent maxima in the loss tangent are found to obey an Arrhenius law with activation energy ∼1 eV for both the samples. The frequency-dependent electrical data are also analyzed in the framework of conductivity formalism. Magnetization of the samples are measured under the field cooled (FC) and zero field cooled (ZFC) modes in the temperature range from 5 K to 300 K applying a magnetic field of 500 Oe. The FC and ZFC susceptibilities show that BE is a Van Vleck paramagnetic material with antiferromagnetic coupling at low temperature whereas BG is an anti-ferromagnetic system. The results are substantiated by the M–H loops of the materials taken at 5 K in the ZFC mode. - Highlights: • BiEuO{sub 3} (BE) and BiGdO{sub 3} (BG) are synthesized by the solid-state reaction technique. • Raman spectra of the samples show five vibrational modes for both the samples. • Cole–Cole model is used to explain the dielectric relaxation in the material. • The activation energy of the material is found to be ∼1 eV.
Heisenberg Honeycombs Solve Veneziano Puzzle
Kholodenko, A L
2006-01-01
In this paper we reformulate some results obtained by Heisenberg into modern mathematical language of honeycombs. This language was developed in connection with complete solution of the Horn conjecture problem. Such a reformulation is done with the purpose of posing and solving the following problem. Is by analysing the (spectroscopic) experimental data it possible to restore the underlying microscopic physical model generating these data? Development of Heisenberg's ideas happens to be the most useful for this purpose. Solution is facilitated by our earlier developed string-theoretic formalism. In this paper only qualitative arguments are presented (with few exceptions). These arguments provide enough evidence that the underelying microscopic model compatible with Veneziano-type amplitudes is the standard (i.e. non supersymmetric!) QCD. In addition, usefulness of the formalism is illustrated on numerous examples such as physically motivated solution of the saturation conjecture, derivation of the Yang-Baxter...
Conjugacy classes in discrete Heisenberg groups
Energy Technology Data Exchange (ETDEWEB)
Budylin, R Ya [Steklov Mathematical Institute of Russian Academy of Sciences (Russian Federation)
2014-08-01
We study an extension of a discrete Heisenberg group coming from the theory of loop groups and find invariants of conjugacy classes in this group. In some cases, including the case of the integer Heisenberg group, we make these invariants more explicit. Bibliography: 4 titles.
Euler-Heisenberg lagrangian through Krein regularization
Refaei, A
2013-01-01
The Euler-Heisenberg effective action at the one-loop for a constant electromagnetic field is derived in Krein space quantization with Ford's idea of uctuated light-cone. In this work we present a perturbative, but convergent solution of the effective action. Without using any renormalization procedure, the result coincides with the famous renormalized Euler-Heisenberg action.
Integrability of Nonholonomic Heisenberg Type Systems
Grigoryev, Yury A.; Sozonov, Alexey P.; Tsiganov, Andrey V.
2016-11-01
We show that some modern geometric methods of Hamiltonian dynamics can be directly applied to the nonholonomic Heisenberg type systems. As an example we present characteristic Killing tensors, compatible Poisson brackets, Lax matrices and classical r-matrices for the conformally Hamiltonian vector fields obtained in a process of reduction of Hamiltonian vector fields by a nonholonomic constraint associated with the Heisenberg system.
Revisiting Riesz transforms on Heisenberg groups
Sanjay, P K
2011-01-01
We characterise higher order Riesz transforms on the Heisenberg group and also show that they satisfy dimension-free bounds under some assumptions on the multipliers. Using transfer- ence theorems, we deduce boundedness theorems for Riesz trans- forms on the reduced Heisenberg group and hence also for the Riesz transforms associated to multiple Hermite and Laguerre ex- pansions.
Theory of disordered Heisenberg ferromagnets
Stubbs, R. M.
1973-01-01
A Green's function technique is used to calculate the magnetic properties of Heisenberg ferromagnets in which the exchange interactions deviate randomly in strength from the mean interaction. Systems of sc, bcc, and fcc topologies and of general spin values are treated. Disorder produces marked effects in the density of spin wave states, in the form of enhancement of the low-energy density and extension of the energy band to higher values. The spontaneous magnetization and the Curie temperature decrease with increasing disorder. The effects of disorder are shown to be more pronounced in the ferromagnetic than in the paramagnetic phase.
Heisenberg limit superradiant superresolving metrology.
Wang, Da-Wei; Scully, Marlan O
2014-08-22
We propose a superradiant metrology technique to achieve the Heisenberg limit superresolving displacement measurement by encoding multiple light momenta into a three-level atomic ensemble. We use 2N coherent pulses to prepare a single excitation superradiant state in a superposition of two timed Dicke states that are 4N light momenta apart in momentum space. The phase difference between these two states induced by a uniform displacement of the atomic ensemble has 1/4N sensitivity. Experiments are proposed in crystals and in ultracold atoms.
Multipartite Entanglement in Heisenberg Model
Institute of Scientific and Technical Information of China (English)
WU Hao; REN Jie; FAN Hong-Yi; ZHU Shi-Qun
2008-01-01
The effects of anisotropy and magnetic field on multipaxtite entanglement of ground state in Heisenberg XY model axe investigated. The multipaxtite entanglement increases as a function of the inverse strength of the external field when the degree of anisotropy is finite. There axe two peaks when the degree of anisotropy is γ =± 1. When the degree of anisotropy increases further, the multipartite entanglement will decrease and tend to a constant. The threshold of the inverse strength of the external field for generating multipaxtite entanglement generally decreases with the increasing of qubits.
Quantum Entanglement in Heisenberg Antiferromagnets
Subramanian, V
2004-01-01
Entanglement sharing among pairs of spins in Heisenberg antiferromagnets is investigated using the concurrence measure. For a nondegenerate S=0 ground state, a simple formula relates the concurrence to the diagonal correlation function. The concurrence length is seen to be extremely short. A few finite clusters are studied numerically, to see the trend in higher dimensions. It is argued that nearest-neighbour concurrence is zero for triangular and Kagome lattices. The concurrences in the maximal-spin states are explicitly calculated, where the concurrence averaged over all pairs is larger than the S=0 states.
Quenching the haldane gap in spin-1 Heisenberg antiferromagnets.
Wierschem, Keola; Sengupta, Pinaki
2014-06-20
We consider a quasi-one-dimensional system of spin-1 Heisenberg antiferromagnetic chains in two-dimensional and three-dimensional hypercubic lattices with interchain coupling J and uniaxial single-ion anisotropy D. Using large-scale numerical simulations, we map out the J-D phase diagram and investigate the low-lying excitations of the Haldane phase in the J≪1 limit. We also provide direct evidence that the Haldane phase remains a nontrivial symmetry-protected topological state for small but finite J.
Valence bond and von Neumann entanglement entropy in Heisenberg ladders.
Kallin, Ann B; González, Iván; Hastings, Matthew B; Melko, Roger G
2009-09-11
We present a direct comparison of the recently proposed valence bond entanglement entropy and the von Neumann entanglement entropy on spin-1/2 Heisenberg systems using quantum Monte Carlo and density-matrix renormalization group simulations. For one-dimensional chains we show that the valence bond entropy can be either less or greater than the von Neumann entropy; hence, it cannot provide a bound on the latter. On ladder geometries, simulations with up to seven legs are sufficient to indicate that the von Neumann entropy in two dimensions obeys an area law, even though the valence bond entanglement entropy has a multiplicative logarithmic correction.
Yang, Chen Ning
2013-05-01
Werner Heisenberg was one of the greatest physicists of all times. When he started out as a young research worker, the world of physics was in a very confused and frustrating state, which Abraham Pais has described1 as: It was the spring of hope, it was the winter of despair using Charles Dickens' words in A Tale of Two Cities. People were playing a guessing game: There were from time to time great triumphs in proposing, through sheer intuition, make-shift schemes that amazingly explained some regularities in spectral physics, leading to joy. But invariably such successes would be followed by further work which reveal the inconsistency or inadequacy of the new scheme, leading to despair...
Sub-Heisenberg estimation strategies are ineffective.
Giovannetti, Vittorio; Maccone, Lorenzo
2012-05-25
In interferometry, sub-Heisenberg strategies claim to achieve a phase estimation error smaller than the inverse of the mean number of photons employed (Heisenberg bound). Here we show that one can achieve a comparable precision without performing any measurement, just using the large prior information that sub-Heisenberg strategies require. For uniform prior (i.e., no prior information), we prove that these strategies cannot achieve more than a fixed gain of about 1.73 over Heisenberg-limited interferometry. Analogous results hold for arbitrary single-mode prior distributions. These results extend also beyond interferometry: the effective error in estimating any parameter is lower bounded by a quantity proportional to the inverse expectation value (above a ground state) of the generator of translations of the parameter.
Gedagtes oor die onbepaaldheidsbeginsel van Heisenberg
Directory of Open Access Journals (Sweden)
P. H. Stoker
1955-03-01
Full Text Available Van filosofiesc syde en ook deur populariserende skrywers is daar al baie geskryf oor die onbepaaldheidsbeginsel in die Fisika, wat deur Heisenberg in die twintiger jare na vore gebring is.
Modified Heisenberg Ferromagnet Model and Integrable Equation
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
We investigate some integrable modified Heisenberg ferromagnet models by using the prolongation structure theory. Through associating them with the motion of curve in Minkowski space, the corresponding coupled integrable equations are presented.
Quantification of entanglement from magnetic susceptibility for a Heisenberg spin 1/2 system
Energy Technology Data Exchange (ETDEWEB)
Chakraborty, Tanmoy; Singh, Harkirat; Das, Diptaranjan; Sen, Tamal K. [Indian Institute of Science Education and Research (IISER) Kolkata, Mohanpur Campus, PO BCKV Campus Main Office, Mohanpur – 741252, Nadia, West Bengal (India); Mitra, Chiranjib, E-mail: chiranjib@iiserkol.ac.in [Indian Institute of Science Education and Research (IISER) Kolkata, Mohanpur Campus, PO BCKV Campus Main Office, Mohanpur – 741252, Nadia, West Bengal (India)
2012-10-01
We report temperature and magnetic field dependent magnetization and quantification of entanglement from the experimental data for dichloro (thiazole) copper (II), a Heisenberg spin chain system. The plot of magnetic susceptibility vs. temperature indicates an infinite spin chain. Isothermal magnetization measurements (as functions of magnetic field) were performed at various temperatures below the antiferromagnetic (AFM) ordering, where the AFM correlations persist significantly. These magnetization curves are fitted to the Bonner–Fisher model. Magnetic susceptibility is used as an entanglement witness to quantify the amount of entanglement in the system. -- Highlights: ► Magnetic properties of a Heisenberg spin chain system are studied. ► Experimental data is fitted to theoretical models. ► Magnetic susceptibility is used as a macroscopic witness of entanglement. ► Entanglement is extracted from experimental data.
Pairwise entanglement and local polarization of Heisenberg model
Institute of Scientific and Technical Information of China (English)
2008-01-01
The characteristics of pairwise entanglement and local polarization (LP) are dis-cussed by studying the ground state (states) of the Heisenberg XX model. The re-sults show that: the ground state (states) is (are) composed of the micro states with the minimal polarization (0 for even qubit and 1/2 for odd qubit); LP and the prob-ability of the micro state have an intimate relation, i.e. the stronger the LP, the smaller the probability, and the same LP corresponds to the same probability; the pairwise entanglement of the ground state is the biggest in all eigenvectors. It is found that the pairwise entanglement is decreased by the state degeneracy and the system size. The concurrence approaches a fixed value of about 0.3412 (for odd-qubit chain) or 0.3491 (for even-qubit chain) if the qubit number is large enough.
The structure and spectrum of Heisenberg odometers
Lightwood, Samuel; Ugarcovici, Ilie
2011-01-01
In recent work Cortez and Petite defined odometer actions of discrete, finitely generated and residually finite groups G. In this paper we focus on the case where G is the discrete Heisenberg group. We prove a structure theorem for finite index subgroups of the Heisenberg group based on their geometry when they are considered as subsets of Z^3. We provide a complete classification of Heisenberg odometers based on the structure of their defining subgroups and we provide examples of each class. Mackey has shown that all such actions have discrete spectrum, i.e. that the unitary operator associated to the dynamical system admits a decomposition into finite dimensional, irreducible representations of the group G. Here we provide an explicit proof of this fact for general G odometers. Our proof allows us to define explicitly those representations of the Heisenberg group which appear in the spectral decomposition of a Heisenberg odometer, as a function of the defining subgroups. Along the way we also provide necess...
Heisenberg XXX model with general boundaries: Eigenvectors from Algebraic Bethe ansatz
Belliard, S
2013-01-01
We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes the usual form of a product of operators acting on a particular vector except that the number of operators is equal to the length of the chain. We prove this result for the chains with small length. We obtain also an off-shell equation (i.e. satisfied without the Bethe equations) formally similar to the ones obtained in the periodic case or with diagonal boundaries.
Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz
Directory of Open Access Journals (Sweden)
Samuel Belliard
2013-11-01
Full Text Available We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes the usual form of a product of operators acting on a particular vector except that the number of operators is equal to the length of the chain. We prove this result for the chains with small length. We obtain also an off-shell equation (i.e. satisfied without the Bethe equations formally similar to the ones obtained in the periodic case or with diagonal boundaries.
Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz
Belliard, Samuel; Crampé, Nicolas
2013-11-01
We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes the usual form of a product of operators acting on a particular vector except that the number of operators is equal to the length of the chain. We prove this result for the chains with small length. We obtain also an off-shell equation (i.e. satisfied without the Bethe equations) formally similar to the ones obtained in the periodic case or with diagonal boundaries.
THE HEAT KERNEL ON THE CAYLEY HEISENBERG GROUP
Institute of Scientific and Technical Information of China (English)
Luan Jingwen; Zhu Fuliu
2005-01-01
The authors obtain an explicit expression of the heat kernel for the Cayley Heisenberg group of order n by using the stochastic integral method of Gaveau. Apart from the standard Heisenberg group and the quaternionic Heisenberg group, this is the only nilpotent Lie group on which an explicit formula for the heat kernel has been obtained.
Aspects of universally valid Heisenberg uncertainty relation
Fujikawa, Kazuo
2012-01-01
A numerical illustration of a universally valid Heisenberg uncertainty relation, which was proposed recently, is presented by using the experimental data on spin-measurements by J. Erhart, et al.[ Nature Phys. {\\bf 8}, 185 (2012)]. This uncertainty relation is closely related to a modified form of the Arthurs-Kelly uncertainty relation which is also tested by the spin-measurements. The universally valid Heisenberg uncertainty relation always holds, but both the modified Arthurs-Kelly uncertainty relation and Heisenberg's error-disturbance relation proposed by Ozawa, which was analyzed in the original experiment, fail in the present context of spin-measurements, and the cause of their failure is identified with the assumptions of unbiased measurement and disturbance. It is also shown that all the universally valid uncertainty relations are derived from Robertson's relation and thus the essence of the uncertainty relation is exhausted by Robertson's relation as is widely accepted.
Correlation functions of the antiferromagnetic Heisenberg model using a modified Lanczos method
Gagliano, Eduardo R.; Dagotto, Elbio; Moreo, Adriana; Alcaraz, Francisco C.
1986-08-01
Using a modified Lanczos algorithm, we study the correlation functions in the ground state of the one-dimensional antiferromagnetic Heisenberg model. We obtain numerical results for rings up to 24 sites. There are no indications of the anomalous behavior of these correlation functions recently observed in chains with 16 sites. We also present a pedagogical description of the hashing technique which is an efficient algorithm for searching and storage purposes.
Influence of Non-Uniform Magnetic Field on Quantum Teleportation in Heisenberg XY Model
Institute of Scientific and Technical Information of China (English)
SHAO Bin; YANG Tie-jian; ZHAO Yue-hong; ZOU Jian
2007-01-01
By considering the intrinsic decoherence, the validity of quantum teleportation of a two-qubit 1D Heisenberg XY chain in a non-uniform external magnetic field is studied. The fidelity as the measurement of a possible quantum teleportation is calculated and the effects of the non-uniform magnetic field and the intrinsic decoherence are discussed. It is found that anti-parallel magnetic field is more favorable for teleportation and the fidelity is suppressed by the intrinsic decoherence.
Classifying tight Weyl-Heisenberg frames
DEFF Research Database (Denmark)
Cazsazza, P.; Janssen, A. J. E. M.; Christensen, Ole
1999-01-01
A Weyl-Heisenberg frame for L^2(R) is a frame consisting of translates and modulates of a fixed function. In this paper we give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down explicitly all functions g for which all translates and modula......A Weyl-Heisenberg frame for L^2(R) is a frame consisting of translates and modulates of a fixed function. In this paper we give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down explicitly all functions g for which all translates...
Extensions of the Heisenberg-Weyl inequality
Directory of Open Access Journals (Sweden)
H. P. Heinig
1986-01-01
Full Text Available In this paper a number of generalizations of the classical Heisenberg-Weyl uncertainty inequality are given. We prove the n-dimensional Hirschman entropy inequality (Theorem 2.1 from the optimal form of the Hausdorff-Young theorem and deduce a higher dimensional uncertainty inequality (Theorem 2.2. From a general weighted form of the Hausdorff-Young theorem, a one-dimensional weighted entropy inequality is proved and some weighted forms of the Heisenberg-Weyl inequalities are given.
Anisotropic Heisenberg model in thin film geometry
Energy Technology Data Exchange (ETDEWEB)
Akıncı, Ümit
2014-01-01
The effect of the anisotropy in the exchange interaction on the phase diagrams and magnetization behavior of the Heisenberg thin film has been investigated with effective field formulation in a two spin cluster using the decoupling approximation. Phase diagrams and magnetization behaviors have been obtained for several different cases, by grouping the systems in accordance with, whether the surfaces/interior of the film has anisotropic exchange interaction or not. - Highlights: • Phase diagrams of the anisotropic Heisenberg model on the thin film obtained • Dependence of the critical properties on the film thickness obtained • Effect of the anisotropy on the magnetic properties obtained.
More on generalized Heisenberg ferromagnet models
Oh, P; Oh, Phillial; Park, Q Han
1996-01-01
We generalize the integrable Heisenberg ferromagnet model according to each Hermitian symmetric spaces and address various new aspects of the generalized model. Using the first order formalism of generalized spins which are defined on the coadjoint orbits of arbitrary groups, we construct a Lagrangian of the generalized model from which we obtain the Hamiltonian structure explicitly in the case of CP(N-1) orbit. The gauge equivalence between the generalized Heisenberg ferromagnet and the nonlinear Schr\\"{o}dinger models is given. Using the equivalence, we find infinitely many conserved integrals of both models.
Rojas, Onofre; Strečka, J.; de Souza, S. M.
2016-11-01
The spin-1/2 Ising-Heisenberg two-leg ladder accounting for alternating Ising and Heisenberg inter-leg couplings in addition to the Ising intra-leg coupling is rigorously mapped onto to a mixed spin-(3/2,1/2) Ising-Heisenberg diamond chain with the nodal Ising spins S = 3 / 2 and the interstitial spin-1/2 Heisenberg dimers. The latter effective model with higher-order interactions between the nodal and interstitial spins is subsequently exactly solved within the transfer-matrix method. The model under investigation exhibits five different ground states: ferromagnetic, antiferromagnetic, superantiferromagnetic and two types of frustrated ground states with a non-zero residual entropy. A detailed study of thermodynamic properties reveals an anomalous specific-heat peak at low enough temperatures, which is strongly reminiscent because of its extraordinary height and sharpness to an anomaly accompanying a phase transition. It is convincingly evidenced, however, that the anomalous peak in the specific heat is finite and it comes from vigorous thermal excitations from a two-fold degenerate ground state towards a macroscopically degenerate excited state. Thermal entanglement between the nearest-neighbor Heisenberg spins is also comprehensively explored by taking advantage of the concurrence. The threshold temperature delimiting a boundary between the entangled and disentangled parameter space may show presence of a peculiar temperature reentrance.
Heisenberg algebra for noncommutative Landau problem
Li, Kang; Cao, Xiao-Hua; Wang, Dong-Yan
2006-10-01
The Landau problem on non-commutative quantum mechanics is studied, where the Heisenberg algebra and the Landau energy levels as well as the non-commutative angular momentum are constructed in detail in non-commutative space and non-commutative phase space respectively.
Constant Angle Surfaces in the Heisenberg Group
Institute of Scientific and Technical Information of China (English)
Johan FASTENAKELS; Marian Ioan MUNTEANU; Joeri VAN DER VEKEN
2011-01-01
In this article we extend the notion of constant angle surfaces in S2 × R and H2 × R to general Bianchi-Cartan-Vranceanu spaces. We show that these surfaces have constant Gaussian curvature and we give a complete local classification in the Heisenberg group.
Lanzani-Stein inequalities in Heisenberg groups
Directory of Open Access Journals (Sweden)
Annalisa Baldi
2013-12-01
Full Text Available Lanzani & Stein consider a class of div-curl inequalities in de Rham's complex. In this note we examine the natural counterpart of that kind of inequalities for dierential forms in Heisenberg groups H1 and H2.
Two-Dimensional Toda-Heisenberg Lattice
Directory of Open Access Journals (Sweden)
Vadim E. Vekslerchik
2013-06-01
Full Text Available We consider a nonlinear model that is a combination of the anisotropic two-dimensional classical Heisenberg and Toda-like lattices. In the framework of the Hirota direct approach, we present the field equations of this model as a bilinear system, which is closely related to the Ablowitz-Ladik hierarchy, and derive its N-soliton solutions.
Heisenberg: Paralleling Scientific and Historical Methods
Cofield, Calla
2007-04-01
Werner Heisenberg is an important historical subject within the physics community partly because his actions as a human being are discussed nearly as often as his work as a physicist. But does the scientific community establish it's historical ideas with the same methods and standards as it's scientific conclusions? I interviewed Heisenberg's son, Jochen Heisenberg, a professor of physics at UNH. Despite a great amount of literature on Werner Heisenberg, only one historian has interviewed Jochen about his father and few have interviewed Werner's wife. Nature is mysterious and unpredictable, but it doesn't lie or distort like humans, and we believe it can give ``honest'' results. But are we keeping the same standards with history that we do with science? Are we holding historians to these standards and if not, is it up to scientists to not only be keepers of scientific understanding, but historical understanding as well? Shouldn't we record history by using the scientific method, by weighing the best sources of data differently than the less reliable, and are we right to be as stubborn about changing our views on history as we are about changing our views on nature?
Heisenberg algebra for noncommutative Landau problem
Institute of Scientific and Technical Information of China (English)
Li Kang; Cao Xiao-Hua; Wang Dong-Yan
2006-01-01
The Landau problem on non-commutative quantum mechanics is studied, where the Heisenberg algebra and the Landau energy levels as well as the non-commutative angular momentum are constructed in detail in non-commutative space and non-commutative phase space respectively.
Polarizability tensor and Kramers-Heisenberg induction
Wijers, C.M.J.
2004-01-01
A general expression for the semiclassical, nonrelativistic linear polarizability of an arbitrary volume element V has been derived in the long wavelength approximation. The derivation starts from the expectation value of the dipole strength, as in the original Kramers-Heisenberg paper about optical
Watson-Crick pairing, the Heisenberg group and Milnor invariants.
Gadgil, Siddhartha
2009-07-01
We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which we call the Heisenberg invariant. The Heisenberg invariant, which is an integer, can be interpreted in terms of the Heisenberg group as well as in terms of lattice paths. We show that the Heisenberg invariant gives a lower bound on the number of unpaired bases in an RNA secondary structure. We also show that the Heisenberg invariant can predict allosteric structures for RNA. Namely, if the Heisenberg invariant is large, then there are widely separated local maxima (i.e., allosteric structures) for the number of Watson-Crick pairs found.
Watson-Crick pairing, the Heisenberg group and Milnor invariants
Gadgil, Siddhartha
2008-01-01
We study the secondary structure of RNA determined by Watson-Crick pairing without pseudo-knots using Milnor invariants of links. We focus on the first non-trivial invariant, which we call the Heisenberg invariant. The Heisenberg invariant, which is an integer, can be interpreted in terms of the Heisenberg group as well as in terms of lattice paths. We show that the Heisenberg invariant gives a lower bound on the number of unpaired bases in an RNA secondary structure. We also show that the Heisenberg invariant can predict \\emph{allosteric structures} for RNA. Namely, if the Heisenberg invariant is large, then there are widely separated local maxima (i.e., allosteric structures) for the number of Watson-Crick pairs found.
Bond diluted anisotropic quantum Heisenberg model
Energy Technology Data Exchange (ETDEWEB)
Akıncı, Ümit, E-mail: umit.akinci@deu.edu.tr
2013-10-15
Effects of the bond dilution on the critical temperatures, phase diagrams and the magnetization behaviors of the isotropic and anisotropic quantum Heisenberg model have been investigated in detail. For the isotropic case, bond percolation threshold values have been determined for several numbers of two (2D) and three (3D) dimensional lattices. In order to investigate the effect of the anisotropy in the exchange interaction on the results obtained for the isotropic model, a detailed investigation has been made on a honeycomb lattice. Some interesting results, such as second order reentrant phenomena in the phase diagrams have been found. - Highlights: • Anisotropic quantum Heisenberg model with bond dilution investigated. • Bond percolation threshold values given for 2D and 3D lattices in isotropic case. • Phase diagrams and ground state magnetizations investigated in detail. • Variation of the bond percolation threshold values with anisotropy determined.
Integrable Heisenberg Ferromagnet Equations with self-consistent potentials
Zhunussova, Zh Kh; Tungushbaeva, D I; Mamyrbekova, G K; Nugmanova, G N; Myrzakulov, R
2013-01-01
In this paper, we consider some integrable Heisenberg Ferromagnet Equations with self-consistent potentials. We study their Lax representations. In particular we give their equivalent counterparts which are nonlinear Schr\\"odinger type equations. We present the integrable reductions of the Heisenberg Ferromagnet Equations with self-consistent potentials. These integrable Heisenberg Ferromagnet Equations with self-consistent potentials describe nonlinear waves in ferromagnets with magnetic fields.
Mean size formula of wavelet subdivision tree on Heisenberg group
Institute of Scientific and Technical Information of China (English)
WANG Guo-mao
2008-01-01
The purpose of this paper is to investigate the mean size formula of wavelet packets (wavelet subdivision tree) on Heisenberg group. The formula is given in terms of the p-norm joint spectral radius. The vector refinement equations on Heisenberg group and the subdivision tree on the Heisenberg group are discussed. The mean size formula of wavelet packets can be used to describe the asymptotic behavior of norm of the subdivision tree.
Weyl-Heisenberg frames for subspaces
DEFF Research Database (Denmark)
Christensen, Ole
2001-01-01
A Weyl-Heisenberg frame {E(mb)T(na)g}(m, n Z) = {e(2 pi imb(.)) g(.-na)}(m, n is an element of Z) for L-2 (R) allows every function f is an element of L-2(R) to be written as an infinite linear combination of translated and modulated versions of the fixed function g is an element of L-2(R...
Controllable entanglement sudden birth of Heisenberg spins
Institute of Scientific and Technical Information of China (English)
ZHENG Qiang; ZHI Qi-Jun; ZHANG Xiao-ping; REN Zhong-Zhou
2011-01-01
We investigate the Entanglement Sudden Birth (ESB) of two Heisenberg spins A and B. The third controller, qutrit C is introduced, which only has the Dzyaloshinskii-Moriya (DM) spin-orbit interaction with qubit B. We find that the DM interaction is necessary to induce the Entanglement Sudden Birth of the system qubits A and B, and the initial states of the system qubits and the qurit C are also important to control its Entanglement Sudden Birth.
Isodiametric sets in the Heisenberg group
Leonardi, Gian Paolo; Rigot, Severine; Vittone, Davide
2010-01-01
In the sub-Riemannian Heisenberg group equipped with its Carnot-Caratheodory metric and with a Haar measure, we consider isodiametric sets, i.e. sets maximizing the measure among all sets with a given diameter. In particular, given an isodiametric set, and up to negligible sets, we prove that its boundary is given by the graphs of two locally Lipschitz functions. Moreover, in the restricted class of rotationally invariant sets, we give a quite complete characterization of any compact (rotatio...
Invariant indentities in the Heisenberg algebra
Turbiner, A V
1994-01-01
Polynomial relations between the generators of q--deformed Heisenberg algebra invariant under the quantization and q-deformation are discovered. One of the examples of such relations is the following: if two elements a and b, obeying the relation \\[ ab - q ba = p, \\] where p, q are any complex numbers, then for any p,q and natural n \\[ (aba)^n = a^n b^n a^n \\
SUGRA new inflation with Heisenberg symmetry
Energy Technology Data Exchange (ETDEWEB)
Antusch, Stefan; Cefalà, Francesco, E-mail: f.cefala@unibas.ch, E-mail: stefan.antusch@unibas.ch [Department of Physics, University of Basel, Klingelbergstr. 82, CH-4056 Basel (Switzerland)
2013-10-01
We propose a realisation of ''new inflation'' in supergravity (SUGRA), where the flatness of the inflaton potential is protected by a Heisenberg symmetry. Inflation can be associated with a particle physics phase transition, with the inflaton being a (D-flat) direction of Higgs fields which break some symmetry at high energies, e.g. of GUT Higgs fields or of Higgs fields for flavour symmetry breaking. This is possible since compared to a shift symmetry, which is usually used to protect a flat inflaton potential, the Heisenberg symmetry is compatible with a (gauge) non-singlet inflaton field. In contrast to conventional new inflation models in SUGRA, where the predictions depend on unknown parameters of the Kaehler potential, the model with Heisenberg symmetry makes discrete predictions for the primordial perturbation parameters which depend only on the order n at which the inflaton appears in the effective superpotential. The predictions for the spectral index n{sub s} can be close to the best-fit value of the latest Planck 2013 results.
SUGRA New Inflation with Heisenberg Symmetry
Antusch, Stefan
2013-01-01
We propose a realisation of 'new inflation' in supergravity (SUGRA), where the flatness of the inflaton potential is protected by a Heisenberg symmetry. Inflation can be associated with a particle physics phase transition, with the inflaton being a (D-flat) direction of Higgs fields which break some symmetry at high energies, e.g. of GUT Higgs fields or of Higgs fields for flavour symmetry breaking. This is possible since compared to a shift symmetry, which is usually used to protect a flat inflaton potential, the Heisenberg symmetry is compatible with a (gauge) non-singlet inflaton field. In contrast to conventional new inflation models in SUGRA, where the predictions depend on unknown parameters of the K"ahler potential, the model with Heisenberg symmetry makes discrete predictions for the primordial perturbation parameters which depend only on the order n at which the inflaton appears in the effective superpotential. The predictions for the spectral index n_s can be close to the best-fit value of the lates...
Quantum spin liquid ground states of the Heisenberg-Kitaev model on the triangular lattice
Kos, Pavel; Punk, Matthias
2017-01-01
We study quantum disordered ground states of the two-dimensional Heisenberg-Kitaev model on the triangular lattice using a Schwinger boson approach. Our aim is to identify and characterize potential gapped quantum spin liquid phases that are stabilized by anisotropic Kitaev interactions. For antiferromagnetic Heisenberg and Kitaev couplings and sufficiently small spin S , we find three different symmetric Z2 spin liquid phases, separated by two continuous quantum phase transitions. Interestingly, the gap of elementary excitations remains finite throughout the transitions. The first spin liquid phase corresponds to the well-known zero-flux state in the Heisenberg limit, which is stable with respect to small Kitaev couplings and develops 120∘ order in the semiclassical limit at large S . In the opposite Kitaev limit, we find a different spin liquid ground state, which is a quantum disordered version of a magnetically ordered state with antiferromagnetic chains, in accordance with results in the classical limit. Finally, at intermediate couplings, we find a spin liquid state with unusual spin correlations. Upon spinon condensation, this state develops Bragg peaks at incommensurate momenta in close analogy to the magnetically ordered Z2 vortex crystal phase, which has been analyzed in recent theoretical works.
Institute of Scientific and Technical Information of China (English)
ZHENG Qiang; ZHI Qi-Jun; ZHANG Xiao-Ping; REN Zhong-Zhou
2011-01-01
We investigate the Entanglement Sudden Birth （ESB） of two Heisenberg spins A and B. The third controller, qutrit C is introduced, which only has the Dzyaloshinskii-Moriya （DM） spin-orbit interaction with qubit B. We find that the DM interaction is necessa
Nonlinear Liouville Theorem in the Quaternionic Heisenberg Group
Institute of Scientific and Technical Information of China (English)
YANG Qiao-hua; ZHU Fu-liu
2005-01-01
This paper deals with the problem of the type△Hf+fp =0 in quaternionic Heisenberg group, where △H isthe quaternionic Heisenberg Laplacian. It is proved that, under suitable conditions on p and f, the only solution of △Hf+fp =0 is f≡0.
Science 101: What, Exactly, Is the Heisenberg Uncertainty Principle?
Robertson, Bill
2016-01-01
Bill Robertson is the author of the NSTA Press book series, "Stop Faking It! Finally Understanding Science So You Can Teach It." In this month's issue, Robertson describes and explains the Heisenberg Uncertainty Principle. The Heisenberg Uncertainty Principle was discussed on "The Big Bang Theory," the lead character in…
Some Weighted Hardy-Type Inequalities on Anisotropic Heisenberg Groups
Directory of Open Access Journals (Sweden)
Yang Qiao-Hua
2011-01-01
Full Text Available We prove some weighted Hardy type inequalities associated with a class of nonisotropic Greiner-type vector fields on anisotropic Heisenberg groups. As an application, we get some new Hardy type inequalities on anisotropic Heisenberg groups which generalize a result of Yongyang Jin and Yazhou Han.
XYZ Quantum Heisenberg Models with p-Orbital Bosons
DEFF Research Database (Denmark)
Pinheiro, Fernanda; Bruun, Georg; Martikainen, Jani-Petri
2013-01-01
We demonstrate how the spin-1/2 XYZ quantum Heisenberg model can be realized with bosonic atoms loaded in the p band of an optical lattice in the Mott regime. The combination of Bose statistics and the symmetry of the p-orbital wave functions leads to a nonintegrable Heisenberg model...
Heisenberg's Universal (lns)**2 Increase of Total Cross Sections
Dosch, H G; Nicolescu, Basarab
2003-01-01
The (lns)**2 behaviour of total cross-sections, first obtained by Heisenberg 50 years ago, receives now increased interest both on phenomenological and theoretical levels. In this paper we present a modification of the Heisenberg's model in connection with the presence of glueballs and we show that it leads to a realistic description of all existing hadron total cross-section data.
DEFF Research Database (Denmark)
Enderle, M.; Kiefer, K.; Klopperpieper, A.;
2000-01-01
Uniform S = 1 and 1/2 Heisenberg antiferromagnetic chains have a quantum singlet ground state which is an eigenstate of the total spin with S(tot) = 0. However, the 'internal' order of these ground states is quite different, and is reflected in gapless excitations in the S = 1/2 state, while the S...
Classical and quantum anisotropic Heisenberg antiferromagnets
Directory of Open Access Journals (Sweden)
W. Selke
2009-01-01
Full Text Available We study classical and quantum Heisenberg antiferromagnets with exchange anisotropy of XXZ-type and crystal field single-ion terms of quadratic and quartic form in a field. The magnets display a variety of phases, including the spin-flop (or, in the quantum case, spin-liquid and biconical (corresponding, in the quantum lattice gas description, to supersolid phases. Applying ground-state considerations, Monte Carlo and density matrix renormalization group methods, the impact of quantum effects and lattice dimension is analysed. Interesting critical and multicritical behaviour may occur at quantum and thermal phase transitions.
Heisenberg scaling in relativistic quantum metrology
Friis, Nicolai; Fuentes, Ivette; Dür, Wolfgang
2015-01-01
We address the issue of precisely estimating small parameters encoded in a general linear transformation of the modes of a bosonic quantum field. Such Bogoliubov transformations frequently appear in the context of quantum optics. We provide a recipe for computing the quantum Fisher information for arbitrary pure initial states. We show that the maximally achievable precision of estimation is inversely proportional to the squared average particle number, and that such Heisenberg scaling requires non-classical, but not necessarily entangled states. Our method further allows to quantify losses in precision arising from being able to monitor only finitely many modes, for which we identify a lower bound.
The XXZ Heisenberg model on random surfaces
Energy Technology Data Exchange (ETDEWEB)
Ambjørn, J., E-mail: ambjorn@nbi.dk [The Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, DK-2100 Copenhagen (Denmark); Institute for Mathematics, Astrophysics and Particle Physics (IMAPP), Radbaud University Nijmegen, Heyendaalseweg 135, 6525 AJ, Nijmegen (Netherlands); Sedrakyan, A., E-mail: sedrak@nbi.dk [The Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, DK-2100 Copenhagen (Denmark); Yerevan Physics Institute, Br. Alikhanyan str. 2, Yerevan-36 (Armenia)
2013-09-21
We consider integrable models, or in general any model defined by an R-matrix, on random surfaces, which are discretized using random Manhattan lattices. The set of random Manhattan lattices is defined as the set dual to the lattice random surfaces embedded on a regular d-dimensional lattice. They can also be associated with the random graphs of multiparticle scattering nodes. As an example we formulate a random matrix model where the partition function reproduces the annealed average of the XXZ Heisenberg model over all random Manhattan lattices. A technique is presented which reduces the random matrix integration in partition function to an integration over their eigenvalues.
The XXZ Heisenberg model on random surfaces
Ambjorn, J
2013-01-01
We consider integrable models, or in general any model defined by an $R$-matrix, on random surfaces, which are discretized using random Manhattan lattices. The set of random Manhattan lattices is defined as the set dual to the lattice random surfaces embedded on a regular d-dimensional lattice. They can also be associated with the random graphs of multiparticle scattering nodes. As an example we formulate a random matrix model where the partition function reproduces the annealed average of the XXZ Heisenberg model over all random Manhattan lattices. A technique is presented which reduces the random matrix integration in partition function to an integration over their eigenvalues.
Frustrated 3×3 Heisenberg antiferromagnets
Moustanis, P. N.
2016-08-01
The full energy spectrum and the exact thermodynamic results of the antiferromagnetic Heisenberg Hamiltonian of the 3×3 triangular and the frustrated square lattice with periodic boundary conditions and s=1/2 are obtained. To this end the method of hierarchy of algebras is employed. It was found that the ground state of the 3×3 frustrated square lattice is a Resonating Valence Bond (RVB) state. Thermodynamic properties, like the specific heat, magnetic susceptibility, the thermal average of the square of the total Sz and entropy, for these two lattices are presented.
Heisenberg scaling in Gaussian quantum metrology
Friis, Nicolai; Skotiniotis, Michalis; Fuentes, Ivette; Dür, Wolfgang
2015-08-01
We address the issue of precisely estimating small parameters encoded in a general linear transformation of the modes of a bosonic quantum field. Such Bogoliubov transformations frequently appear in the context of quantum optics. We provide a set of instructions for computing the quantum Fisher information for arbitrary pure initial states. We show that the maximally achievable precision of estimation is inversely proportional to the squared average particle number and that such Heisenberg scaling requires nonclassical but not necessarily entangled states. Our method further allows us to quantify losses in precision arising from being able to monitor only finitely many modes, for which we identify a lower bound.
Tsallis Entropy Composition and the Heisenberg Group
Kalogeropoulos, Nikos
2013-03-01
We present an embedding of the Tsallis entropy into the three-dimensional Heisenberg group, in order to understand the meaning of generalized independence as encoded in the Tsallis entropy composition property. We infer that the Tsallis entropy composition induces fractal properties on the underlying Euclidean space. Using a theorem of Milnor/Wolf/Tits/Gromov, we justify why the underlying configuration/phase space of systems described by the Tsallis entropy has polynomial growth for both discrete and Riemannian cases. We provide a geometric framework that elucidates Abe's formula for the Tsallis entropy, in terms the Pansu derivative of a map between sub-Riemannian spaces.
Discrete flavour symmetries from the Heisenberg group
Floratos, E. G.; Leontaris, G. K.
2016-04-01
Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated to the geometry of the compactification manifold and more particularly to the magnetised branes in toroidal compactifications. Motivated by these facts, in this note we propose a unified framework to construct representations of finite discrete family groups based on the automorphisms of the discrete and finite Heisenberg group. We focus in particular, on the PSL2 (p) groups which contain the phenomenologically interesting cases.
Discrete Flavour Symmetries from the Heisenberg Group
Floratos, E G
2015-01-01
Non-abelian discrete symmetries are of particular importance in model building. They are mainly invoked to explain the various fermion mass hierarchies and forbid dangerous superpotential terms. In string models they are usually associated to the geometry of the compactification manifold and more particularly to the magnetised branes in toroidal compactifications. Motivated by these facts, in this note we propose a unified framework to construct representations of finite discrete family groups based on the automorphisms of the discrete and finite Heisenberg group. We focus in particular in the $PSL_2(p)$ groups which contain the phenomenologically interesting cases.
Critical exponents of the classical Heisenberg ferromagnet
Holm, C; Holm, Christian; Janke, Wolfhard
1997-01-01
In a recent letter, R.G. Brown and M. Ciftan (Phys. Rev. Lett. 76, 1352, 1996) reported high precision Monte Carlo (MC) estimates of the static critical exponents of the classical 3D Heisenberg model, which stand in sharp contrast to values obtained by four independent approaches, namely by other recent high statistics MC simulations, high-temperature series analyses, field theoretical methods, and experimental studies. In reply to the above cited work we submitted this paper as a comment to Phys. Rev. Lett.
Heisenberg Model in a Rotating Magnetic Field
Institute of Scientific and Technical Information of China (English)
LIN Qiong-Gui
2005-01-01
We study the Heisenberg model under the influence of a rotating magnetic field. By using a time-dependent unitary transformation, the time evolution operator for the Schrodinger equation is obtained, which involves no chronological product. The spin vectors (mean values of the spin operators) are obtained as explicit functions of time in the most general case. A series of cyclic solutions are presented. The nonadiabatic geometric phases of these cyclic solutions are calculated, and are expressed in terms of the solid angle subtended by the closed trace of the total spin vector, as well as in terms of those of the individual spins.
Generalized Heisenberg algebras and Fibonacci series
Energy Technology Data Exchange (ETDEWEB)
Souza, J de; Curado, E M F; Rego-Monteiro, M A [Centro Brasileiro de Pesquisa Fisicas, Rua Dr. Xavier Sigaud, 150, 22290-180, Rio de Janeiro (Brazil)
2006-08-18
We have constructed a Heisenberg-type algebra generated by the Hamiltonian, the step operators and an auxiliary operator. This algebra describes quantum systems having eigenvalues of the Hamiltonian depending on the eigenvalues of the two previous levels. This happens, for example, for systems having the energy spectrum given by a Fibonacci sequence. Moreover, the algebraic structure depends on the two functions f(x) and g(x). When these two functions are linear we classify, analysing the stability of the fixed points of the functions, the possible representations for this algebra.
Bond-Dilution Effects on Two-Dimensional Spin-Gapped Heisenberg Antiferromagnets
Yasuda, Chitoshi; Todo, Synge; Matsumoto, Munehisa; Takayama, Hajime
2001-01-01
Bond-dilution effects on spin-1/2 spin-gapped Heisenberg antiferromagnets of coupled alternating chains on a square lattice are investigated by means of the quantum Monte Carlo method. It is found that, in contrast with the site-diluted system having an infinitesimal critical concentration, the bond-diluted system has a finite critical concentration of diluted bonds, $x_{c}$, above which the system is in an antiferromagnetic (AF) long-range ordered phase. In the disordered phase below $x_{c}$...
Automorphism Group of a Class of Heisenberg n-Lie Algebras%一类Heisenberg n-李代数的自同构群
Institute of Scientific and Technical Information of China (English)
白瑞蒲; 刘丽丽
2011-01-01
本文主要研究Heisenberg n-李代数的结构.给出了一类(3m+1)-维Heisenberg 3-李代数及(nm+1)-维Heisenberg n-李代数的自同构群.且给出了自同构的具体表达式.%This paper mainly concerns Heisenberg n-Lie algebras. The structure of automorphism groups of (3m+1)-dimensional Heisenberg 3-Lie algebras is determined. The automorphism groups of (mn+1)-dimensional Heisenberg n-Lie algebras are studied; the concrete expression of every automorphism is given.
Geometric Quantum Discord in the Heisenberg XX Model with Three-Spin Interactions
Xie, Yu-Xia; Liu, Jing; Sun, Yu-Hang
2016-11-01
Quantum discord is a resource for quantum information processing tasks, and seeking flexible ways to control it is of practical significance. We investigate the trace distance, Bures distance, and Hellinger distance geometric quantum discords (GQDs) for thermal states of the Heisenberg XX chain with three-spin interactions. The results show that both the XZX + YZY and XZY -YZX types of three-spin interactions can be used to enhance evidently the GQDs for the boundary spins of the chain. The optimal strengths of three-spin interactions for which the maximum enhancement of the GQDs are achieved are strongly dependent on the GQD measures we adopted and the number of spins in the chain.
Geometric Quantum Discord in the Heisenberg XX Model with Three-Spin Interactions
Xie, Yu-Xia; Liu, Jing; Sun, Yu-Hang
2017-02-01
Quantum discord is a resource for quantum information processing tasks, and seeking flexible ways to control it is of practical significance. We investigate the trace distance, Bures distance, and Hellinger distance geometric quantum discords (GQDs) for thermal states of the Heisenberg XX chain with three-spin interactions. The results show that both the XZX + YZY and XZY - YZX types of three-spin interactions can be used to enhance evidently the GQDs for the boundary spins of the chain. The optimal strengths of three-spin interactions for which the maximum enhancement of the GQDs are achieved are strongly dependent on the GQD measures we adopted and the number of spins in the chain.
Heisenberg-limited metrology without entanglement
Energy Technology Data Exchange (ETDEWEB)
Braun, Daniel [Universite de Toulouse, UPS, Laboratoire de Physique Theorique (IRSAMC), F-31062 Toulouse (France); CNRS, LPT (IRSAMC), F-31062 Toulouse (France); Martin, John [Institut de Physique Nucleaire, Atomique et de Spectroscopie, Universite de Liege, 4000 Liege (Belgium)
2012-07-01
It is common experimental practice to improve the signal-to-noise ratio by averaging many measurements of identically prepared systems. If the systems are independent, the overall sensitivity of the measurement, defined as the smallest resolvable change of the quantity under consideration, improves as 1/{radical}(N). Quantum enhanced measurements promise the possibility to improve this scaling behavior. Indeed, if the N systems are initially entangled, one may achieve in principle a 1/N scaling of the sensitivity, known as the ''Heisenberg limit''. Unfortunately, decoherence has so far limited the implementation of such ''quantum enhanced protocols'' to small values of N. Here we show that a setup in which N quantum systems interact with a N+1st system allows one to achieve Heisenberg limited sensitivity, without using or ever creating any entanglement. Local decoherence changes only the prefactor but not the scaling with N. We present a general theoretical framework for this new kind of measurement scheme, and propose a possible application in high precision measurements of the length of an optical cavity.
The internal energies of Heisenberg magnetic systems
Energy Technology Data Exchange (ETDEWEB)
Wang, Huai-Yu, E-mail: wanghuaiyu@mail.tsinghua.edu.cn [Department of Physics, Tsinghua University, Beijing 100084 (China); Zhai, Liang-Jun [Department of Physics, Tsinghua University, Beijing 100084 (China); Qian, Meichun [Department of Physics, Virginia Commonwealth University, Richmond, VA 23284 (United States)
2014-03-15
The internal energies, including transverse and longitudinal parts, of quantum Heisenberg systems for arbitrary spin S are investigated by the double-time Green's function method. The expressions for ferromagnetic (FM) and antiferromagnetic (AFM) systems are derived when one-component of magnetization is considered with the higher order longitudinal correlation functions being carefully treated. An unexpected result is that around the order–disorder transition points the neighboring spins in a FM (AFM) system are more likely longitudinally antiparallel (parallel) than parallel (antiparallel) to each other for S≤3/2 in spite of the FM (AFM) exchange between the spins. This is attributed to the strong quantum fluctuation of the systems with small S values. We also present the expressions of the internal energies of FM systems when the three-component of magnetizations are considered. - Highlights: • We give the best expressions of the internal energies for Heisenberg magnetic systems. • Around transition temperature, the longitudinal correlation energies for magnetic systems are positive due to strong quantum fluctuation. • A system with smaller spin quantum number has a stronger fluctuation even if there is spontaneous magnetization. • The strong quantum fluctuation cannot be totally suppressed by an external magnetic field. • The expressions of the internal energies when the magnetization has three components are given.
Callen-like method for the classical Heisenberg ferromagnet
Campana, L. S.; Cavallo, A.; De Cesare, L.; Esposito, U.; Naddeo, A.
2012-02-01
A study of the d-dimensional classical Heisenberg ferromagnetic model in the presence of a magnetic field is performed within the two-time Green function's framework in classical statistical physics. We extend the well known quantum Callen method to derive analytically a new formula for magnetization. Although this formula is valid for any dimensionality, we focus on one- and three- dimensional models and compare the predictions with those arising from a different expression suggested many years ago in the context of the classical spectral density method. Both frameworks give results in good agreement with the exact numerical transfer-matrix data for the one-dimensional case and with the exact high-temperature-series results for the three-dimensional one. In particular, for the ferromagnetic chain, the zero-field susceptibility results are found to be consistent with the exact analytical ones obtained by M.E. Fisher. However, the formula derived in the present paper provides more accurate predictions in a wide range of temperatures of experimental and numerical interest.
Alécio, Raphael C.; Lyra, Marcelo L.; Strečka, Jozef
2016-11-01
The ground-state phase diagram, magnetization process and bipartite entanglement of the frustrated spin-1/2 Ising-Heisenberg and Heisenberg triangular tube (three-leg ladder) are investigated in a non-zero external magnetic field. The exact ground-state phase diagram of the spin-1/2 Ising-Heisenberg tube with Heisenberg intra-rung and Ising inter-rung couplings consists of six distinct gapped phases, which manifest themselves in a magnetization curve as intermediate plateaus at zero, one-third and two-thirds of the saturation magnetization. Four out of six available ground states exhibit quantum entanglement between two spins from the same triangular unit evidenced by a non-zero concurrence. Density-matrix renormalization group calculations are used in order to construct the ground-state phase diagram of the analogous but purely quantum spin-1/2 Heisenberg tube with Heisenberg intra- and inter-rung couplings, which consists of four gapped and three gapless phases. The Heisenberg tube shows a continuous change of the magnetization instead of a plateau at zero magnetization, while the intermediate one-third and two-thirds plateaus may be present or not in the zero-temperature magnetization curve.
Quench dynamics of the anisotropic Heisenberg model.
Liu, Wenshuo; Andrei, Natan
2014-06-27
We develop an analytical approach for the study of the quench dynamics of the anisotropic Heisenberg model (XXZ model) on the infinite line. We present the exact time-dependent wave functions after a quench in an integral form for any initial state and for any anisotropy Δ by means of a generalized Yudson contour representation. We calculate the evolution of several observables from two particular initial states: starting from a local Néel state we calculate the time evolution of the antiferromagnetic order parameter-staggered magnetization; starting from a state with consecutive flipped spins (1) we calculate the evolution of the local magnetization and express it in terms of the propagation of magnons and bound state excitations, and (2) we predict the evolution of the induced spin currents. These predictions can be confronted with experiments in ultracold gases in optical lattices. We also show how the "string" solutions of Bethe ansatz equations emerge naturally from the contour approach.
SU (N ) Heisenberg model with multicolumn representations
Okubo, Tsuyoshi; Harada, Kenji; Lou, Jie; Kawashima, Naoki
2015-10-01
The SU (N ) symmetric antiferromagnetic Heisenberg model with multicolumn representations on the two-dimensional square lattice is investigated by quantum Monte Carlo simulations. For the representation of a Young diagram with two columns, we confirm that a valence-bond solid (VBS) order appears as soon as the Néel order disappears at N =10 , indicating no intermediate phase. In the case of the representation with three columns, there is no evidence for either the Néel or the VBS ordering for N ≥15 . This is actually consistent with the large-N theory, which predicts that the VBS state immediately follows the Néel state, because the expected spontaneous order is too weak to be detected.
Schur-Weyl Duality for Heisenberg Cosets
Creutzig, Thomas; Linshaw, Andrew R; Ridout, David
2016-01-01
Let $V$ be a simple vertex operator algebra containing a rank $n$ Heisenberg vertex algebra $H$ and let $C=\\text{Com}\\left( {H}, {V}\\right)$ be the coset of ${H}$ in ${V}$. Assuming that the representation categories of interest are vertex tensor categories in the sense of Huang, Lepowsky and Zhang, a Schur-Weyl type duality for both simple and indecomposable but reducible modules is proven. Families of vertex algebra extensions of ${C}$ are found and every simple ${C}$-module is shown to be contained in at least one ${V}$-module. A corollary of this is that if ${V}$ is rational and $C_2$-cofinite and CFT-type, and $\\text{Com}\\left( {C}, {V}\\right)$ is a rational lattice vertex operator algebra, then so is ${C}$. These results are illustrated with many examples and the $C_1$-cofiniteness of certain interesting classes of modules is established.
Fractal dimension in percolating Heisenberg antiferromagnets
Energy Technology Data Exchange (ETDEWEB)
Itoh, S. [Neutron Science Laboratory, High Energy Accelerator Research Organization, Tsukuba 305-0810 (Japan)]. E-mail: shinichi.itoh@kek.jp; Kajimoto, R. [Quantum Beam Science Directorate, Japan Atomic Energy Agency, Tokai 319-1195 (Japan); Adams, M.A. [ISIS Facility, Rutherford Appleton Laboratory, Didcot, Oxon OX11 0QX (United Kingdom); Bull, M.J. [ISIS Facility, Rutherford Appleton Laboratory, Didcot, Oxon OX11 0QX (United Kingdom); Iwasa, K. [Department of Physics, Tohoku University, Sendai 980-8578 (Japan); Aso, N. [Neutron Science Laboratory, Institute for Solid State Physics, University of Tokyo, Tokai 319-1106 (Japan); Yoshizawa, H. [Neutron Science Laboratory, Institute for Solid State Physics, University of Tokyo, Tokai 319-1106 (Japan); Takeuchi, T. [Low Temperature Center, Osaka University, Toyonaka 560-0043 (Japan)
2007-03-15
We investigated static and dynamical properties in the three-dimensional percolating Heisenberg antiferromagnets, RbMn{sub c}Mg{sub 1-c}F{sub 3}, with the magnetic concentration close to the percolation threshold, c{sub P}=0.312, around the superlattice point well below T{sub N}. In neutron diffraction experiment, the wave number dependence of the elastic scattering component was well fitted to q{sup -x}. Magnetic fractons were also studied using inelastic neutron scattering, and the observed fractons showed the dispersion relation of q{sup z}. The determined exponents, x=2.43+/-0.05 and z=2.5+/-0.1, were in good agreement with the fractal dimension (D{sub f}=2.48)
Nocera, A.; Patel, N. D.; Fernandez-Baca, J.; Dagotto, E.; Alvarez, G.
2016-11-01
We study the effects of charge degrees of freedom on the spin excitation dynamics in quasi-one-dimensional magnetic materials. Using the density matrix renormalization group method, we calculate the dynamical spin structure factor of the Hubbard model at half electronic filling on a chain and on a ladder geometry, and compare the results with those obtained using the Heisenberg model, where charge degrees of freedom are considered frozen. For both chains and two-leg ladders, we find that the Hubbard model spectrum qualitatively resembles the Heisenberg spectrum—with low-energy peaks resembling spinonic excitations—already at intermediate on-site repulsion as small as U /t ˜2 -3 , although ratios of peak intensities at different momenta continue evolving with increasing U /t converging only slowly to the Heisenberg limit. We discuss the implications of these results for neutron scattering experiments and we propose criteria to establish the values of U /t of quasi-one-dimensional systems described by one-orbital Hubbard models from experimental information.
RANDOM ATTRACTORS FOR A STOCHASTIC HYDRODYNAMICAL EQUATION IN HEISENBERG PARAMAGNET
Institute of Scientific and Technical Information of China (English)
Guo Boling; Guo Chunxiao; Pu Xueke
2011-01-01
This article studies the asymptotic behaviors of the solution for a stochastic hydrodynamical equation in Heisenberg paramagnet in a two-dimensional periodic domain. We obtain the existence of random attractors in H1.
Heisenberg's Uncertainty Principle and Interpretive Research in Science Education.
Roth, Wolff-Michael
1993-01-01
Heisenberg's uncertainty principle and the derivative notions of interdeterminacy, uncertainty, precision, and observer-observed interaction are discussed and their applications to social science research examined. Implications are drawn for research in science education. (PR)
Smooth Solutions for a Stochastic Hydrodynamical Equation in Heisenberg Paramagnet
Institute of Scientific and Technical Information of China (English)
Xue Ke PU; Bo Ling GUO; Yong Qian HAN
2011-01-01
In this article,we consider a stochastic hydrodynamical equation in Heisenberg paramagnet driven by additive noise.We prove the existence and uniqueness of smooth solutions to this equation with difference method.
Lorentz-violating Euler-Heisenberg effective action
Furtado, J
2014-01-01
In this work, we study the radiative generation of the Lorentz-violating Euler-Heisenberg action, in the weak field approximation. For this, we first consider a nonperturbative calculation in the coefficient $c_{\\mu\
An improved Hardy type inequality on Heisenberg group
Directory of Open Access Journals (Sweden)
Xiao Ying-Xiong
2011-01-01
Full Text Available Abstract Motivated by the work of Ghoussoub and Moradifam, we prove some improved Hardy inequalities on the Heisenberg group ℍ n via Bessel function. Mathematics Subject Classification (2000: Primary 26D10
Semilinear elliptic problems on unbounded subsets of the Heisenberg group
Directory of Open Access Journals (Sweden)
K. Tintarev
2001-03-01
Full Text Available In this paper we discuss the applications of an abstract version of concentration compactness to minimax problems. In particular, we prove the existence of solutions to semilinear elliptic problems on unbounded subsets of the Heisenberg group.
General optimality of the Heisenberg limit for quantum metrology.
Zwierz, Marcin; Pérez-Delgado, Carlos A; Kok, Pieter
2010-10-29
Quantum metrology promises improved sensitivity in parameter estimation over classical procedures. However, there is a debate over the question of how the sensitivity scales with the resources and the number of queries that are used in estimation procedures. Here, we reconcile the physical definition of the relevant resources used in parameter estimation with the information-theoretical scaling in terms of the query complexity of a quantum network. This leads to a completely general optimality proof of the Heisenberg limit for quantum metrology. We give an example of how our proof resolves paradoxes that suggest sensitivities beyond the Heisenberg limit, and we show that the Heisenberg limit is an information-theoretic interpretation of the Margolus-Levitin bound, rather than Heisenberg's uncertainty relation.
Beyond Uncertainty Heisenberg, Quantum Physics, and The Bomb
Cassidy, David C
2010-01-01
Award winning biographer revisits the controversial life of this well known German physicist to shed new light on troubling questions. What can we learn about the relationship of scientific research to state power from Heisenberg's role in Nazi Germany?
Magnetic Properties of Heisenberg Thin Films in an External Field
Institute of Scientific and Technical Information of China (English)
CHEN Hong; ZHANG Jing
2004-01-01
The magnetic properties of Heisenberg ferromagnetic films in an external magnetic field are investigated by means of the variational cumulant expansion (VCE). The magnetization can be in principle calculated analytically as the function of the temperature and the number of atomic layers in the film to an arbitrary order of accuracy in the VCE. We calculate the spontaneous magnetization and coercivity to the third order for spin-1/2 Heisenberg films with simple cubic lattices by using a graphic technique.
Comparison principle for parabolic equations in the Heisenberg group
Directory of Open Access Journals (Sweden)
Thomas Bieske
2005-09-01
Full Text Available We define two notions of viscosity solutions to parabolic equations in the Heisenberg group, depending on whether the test functions concern only the past or both the past and the future. We then exploit the Heisenberg geometry to prove a comparison principle for a class of parabolic equations and show the sufficiency of considering the test functions that concern only the past.
Energy Spectrum Symmetry of Heisenberg Model in Fock Space
Institute of Scientific and Technical Information of China (English)
WANG An-Min; ZHU Ren-Gui
2006-01-01
@@ We extend the BCS paring model with equally spaced energy levels to a general one-dimensional spin-l/2 Heisenberg model. The two well-known symmetries of the Heisenberg model, i.e. permutational and spin-inversion symmetries, no longer exist. However, when jointing these two operations together, we find a new symmetry of energy spectrum between its subspace n and subspace L - n of the Fock space. A rigorous proof is presented.
B-tubular surfaces in Lorentzian Heisenberg Group H3
Directory of Open Access Journals (Sweden)
Talat Körpınar
2015-01-01
Full Text Available In this paper, B-tubular surfaces in terms of biharmonic spacelike new type B-slant helices according to Bishop frame in the Lorentzian Heisenberg group H3 are studied. The Necessary and sufficient conditions for new type B-slant helices to be biharmonic are obtained. B-tubular surfaces in the cLorentzian Heisenberg group H3 are characterized. Additionally, main results in Figures 1, 2, 3 and 4 are illustrated.
Realization of an Ultrasensitive Heisenberg-Limited Interferometer
2006-07-31
used a Monte Carlo simulation program to examine the effect of losses on this highly nonlinear detection scheme, with its experimental imple...is below since many authors do not follow the 200 word limit 14. SUBJECT TERMS quantum optics, nonlinear optics, squeezed states, Heisenberg -limited...Programs 1001 N. Emmett St. P.O. Box 400195 Charlottesville, VA 22904 -4195 Realization of an Ultrasensitive Heisenberg -Limited Interferometer REPORT
Superconformal Quantum Mechanics via Wigner-Heisenberg Algebra
Carrion, H L
2004-01-01
We show the natural relation between the Wigner Hamiltonian and the conformal Hamiltonian, by presenting a model in (super)conformal quantum mechanics with (super)conformal symmetry in the Wigner-Heisenberg algebra picture $ [x,p_{x}]= i(1+c{\\bf P}).$ We define its energy spectrum and construct the Casimir, creation and annihilation operators using the Wigner-Heisenberg algebra. It is also found a super-Hamiltonian of the Calogero interaction's type for a two-particle model.
Quantum crystals and spin chains
Energy Technology Data Exchange (ETDEWEB)
Dijkgraaf, Robbert [KdV Institute for Mathematics, University of Amsterdam, Plantage Muidergracht 24, 1018 TV Amsterdam (Netherlands); Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands); Orlando, Domenico [Institut de Physique, Universite de Neuchatel, Rue Breguet 1, CH-2000 Neuchatel (Switzerland); Reffert, Susanne [Institute for Theoretical Physics, University of Amsterdam, Valckenierstraat 65, 1018 XE Amsterdam (Netherlands)], E-mail: sreffert@gmail.com
2009-04-21
In this article, we discuss the quantum version of the melting crystal corner in one, two, and three dimensions, generalizing the treatment for the quantum dimer model. Using a mapping to spin chains we find that the two-dimensional case (growth of random partitions) is integrable and leads directly to the Hamiltonian of the Heisenberg XXZ ferromagnet. The three-dimensional case of the melting crystal corner is described in terms of a system of coupled XXZ spin chains. We give a conjecture for its mass gap and analyze the system numerically.
Quantum crystals and spin chains
Dijkgraaf, Robbert; Orlando, Domenico; Reffert, Susanne
2009-04-01
In this article, we discuss the quantum version of the melting crystal corner in one, two, and three dimensions, generalizing the treatment for the quantum dimer model. Using a mapping to spin chains we find that the two-dimensional case (growth of random partitions) is integrable and leads directly to the Hamiltonian of the Heisenberg XXZ ferromagnet. The three-dimensional case of the melting crystal corner is described in terms of a system of coupled XXZ spin chains. We give a conjecture for its mass gap and analyze the system numerically.
Automorphism Group of Heisenberg Jordan-Lie Algebra%Heisenberg Jordan-Lie代数的自同构群
Institute of Scientific and Technical Information of China (English)
周佳
2014-01-01
We introduced the notion of Heisenberg Jordan-Lie algebra so as to investigate some subgroups of the automorphism group Aut(H)of Heisenberg Jordan-Lie algebra H.Moreover,we discussed some basic structure of the automorphism group Aut (H ) in the case of H being low-dimensional.%通过给出 Heisenberg Jordan-Lie 代数的定义，得到 Heisenberg Jordan-Lie 代数H 的自同构群Aut(H )的一些子群，并在 H 为低维的情形下，讨论了自同构群 Aut (H )的基本结构。
Modified algebraic Bethe ansatz for XXZ chain on the segment – I: Triangular cases
Directory of Open Access Journals (Sweden)
Samuel Belliard
2015-03-01
Full Text Available The modified algebraic Bethe ansatz, introduced by Crampé and the author [8], is used to characterize the spectral problem of the Heisenberg XXZ spin-12 chain on the segment with lower and upper triangular boundaries. The eigenvalues and the eigenvectors are conjectured. They are characterized by a set of Bethe roots with cardinality equal to N the length of the chain and which satisfies a set of Bethe equations with an additional term. The conjecture follows from exact results for small chains. We also present a factorized formula for the Bethe vectors of the Heisenberg XXZ spin-12 chain on the segment with two upper triangular boundaries.
Non Self-conjugate Strings, Singular Strings and Rigged Configurations in the Heisenberg Model
Deguchi, Tetsuo
2014-01-01
It is observed that there exists a different kind of string solutions in the isotropic Heisenberg spin 1/2 chain starting from $N=12$, where the central rapidity of the odd strings become complex making the strings non self conjugate individually. We show that there are at most (N-2)/2 singular highest weight solutions for M=4, M=5, and for N\\geq 2M and at most (N^2-6N+8)/8 singular solutions for M=6 , M=7 and for N\\geq 2M in an even length chain. Correspondence of the non self conjugate string as well as singular string solutions with the Rigged configurations is also discussed.
Non self-conjugate strings, singular strings and rigged configurations in the Heisenberg model
Deguchi, Tetsuo; Ranjan Giri, Pulak
2015-02-01
We observe a different type of complex solutions in the isotropic spin-1/2 Heisenberg chain starting from N = 12, where the central rapidity of some of the odd-length strings becomes complex so that not all the strings self-conjugate individually. We show that there are at most (N - 2)/2 singular solutions for M = 4, M = 5 down-spins and at most (N2 - 6N + 8)/8 singular solutions for M = 6, M = 7 down-spins in an even-length chain with N ⩾ 2M. Correspondence of the non self-conjugate string solutions and the singular string solutions to the rigged configurations has also been shown.
Time independent universal computing with spin chains: quantum plinko machine
Thompson, K. F.; Gokler, C.; Lloyd, S.; Shor, P. W.
2016-07-01
We present a scheme for universal quantum computing using XY Heisenberg spin chains. Information is encoded into packets propagating down these chains, and they interact with each other to perform universal quantum computation. A circuit using g gate blocks on m qubits can be encoded into chains of length O({g}3+δ {m}3+δ ) for all δ \\gt 0 with vanishingly small error.
New Insights? Heisenberg's visit to Copenhagen in 1941 and the Bohr letters
Gottstein, Klaus
2006-01-01
It is shown that, in contrast to many interpretations in the press, the drafts of Bohr's unsent letters to Heisenberg are not contradicting Heisenberg's description of his famous trip in 1941 to Copenhagen, but are complementary to it.
Nonlinear phonon interferometry at the Heisenberg limit
Cheung, Hil F. H.; Patil, Yogesh Sharad; Chang, Laura; Chakram, Srivatsan; Vengalattore, Mukund
2016-05-01
Interferometers operating at or close to quantum limits of precision have found wide application in tabletop searches for physics beyond the standard model, the study of fundamental forces and symmetries of nature and foundational tests of quantum mechanics. The limits imposed by quantum fluctuations and measurement backaction on conventional interferometers (δϕ 1 /√{ N}) have spurred the development of schemes to circumvent these limits through quantum interference, multiparticle interactions and entanglement. Here, we realize a prominent example of such schemes, the so-called SU(1,1) interferometer, in a fundamentally new platform in which the interfering arms are distinct flexural modes of a millimeter-scale mechanical resonator. We realize up to 15.4(3) dB of noise squeezing and demonstrate the Heisenberg scaling of interferometric sensitivity (δϕ 1 / N), corresponding to a 6-fold improvement in measurement precision over a conventional interferometer. We describe how our work extends the optomechanical toolbox and how it presents new avenues for studies of optomechanical sensing and studies of nonequilibrium dynamics of multimode optomechanical systems. This work was supported by the DARPA QuASAR program through a grant from the ARO, the ARO MURI on non-equilibrium manybody dynamics and an NSF INSPIRE award.
Open timelike curves violate Heisenberg's uncertainty principle.
Pienaar, J L; Ralph, T C; Myers, C R
2013-02-08
Toy models for quantum evolution in the presence of closed timelike curves have gained attention in the recent literature due to the strange effects they predict. The circuits that give rise to these effects appear quite abstract and contrived, as they require nontrivial interactions between the future and past that lead to infinitely recursive equations. We consider the special case in which there is no interaction inside the closed timelike curve, referred to as an open timelike curve (OTC), for which the only local effect is to increase the time elapsed by a clock carried by the system. Remarkably, circuits with access to OTCs are shown to violate Heisenberg's uncertainty principle, allowing perfect state discrimination and perfect cloning of coherent states. The model is extended to wave packets and smoothly recovers standard quantum mechanics in an appropriate physical limit. The analogy with general relativistic time dilation suggests that OTCs provide a novel alternative to existing proposals for the behavior of quantum systems under gravity.
Microscopic Origin of Heisenberg and Non-Heisenberg Exchange Interactions in Ferromagnetic bcc Fe.
Kvashnin, Y O; Cardias, R; Szilva, A; Di Marco, I; Katsnelson, M I; Lichtenstein, A I; Nordström, L; Klautau, A B; Eriksson, O
2016-05-27
By means of first principles calculations, we investigate the nature of exchange coupling in ferromagnetic bcc Fe on a microscopic level. Analyzing the basic electronic structure reveals a drastic difference between the 3d orbitals of E_{g} and T_{2g} symmetries. The latter ones define the shape of the Fermi surface, while the former ones form weakly interacting impurity levels. We demonstrate that, as a result of this, in Fe the T_{2g} orbitals participate in exchange interactions, which are only weakly dependent on the configuration of the spin moments and thus can be classified as Heisenberg-like. These couplings are shown to be driven by Fermi surface nesting. In contrast, for the E_{g} states, the Heisenberg picture breaks down since the corresponding contribution to the exchange interactions is shown to strongly depend on the reference state they are extracted from. Our analysis of the nearest-neighbor coupling indicates that the interactions among E_{g} states are mainly proportional to the corresponding hopping integral and thus can be attributed to be of double-exchange origin. By making a comparison to other magnetic transition metals, we put the results of bcc Fe into context and argue that iron has a unique behavior when it comes to magnetic exchange interactions.
Modified Heisenberg model for the zig-zag structure in multiferroic RMn2O5
Bahoosh, Safa Golrokh; Wesselinowa, Julia M.; Trimper, Steffen
2015-08-01
The class of RMn2O5 (R = Ho, Tb, Y, Eu) compounds offers multiferroic properties where the refined magnetic zig-zag order breaks the inversion symmetry. Varying the temperature, the system undergoes a magnetic and a subsequent ferroelectric phase transition where the ferroelectricity is magnetically induced. We propose a modified anisotropic Heisenberg model that can be used as a tractable analytical model studying the properties of those antiferromagnetic zig-zag spin chains. Based on a finite temperature Green's function method, it is shown that the polarization is induced solely by different exchange couplings of the two different Mn4+ and Mn3+ magnetic ions. We calculate the excitation energy of the spin system for finite temperatures, which for its part determines the temperature dependent magnetization and polarization. The ferroelectric phase transition is manifested as a kink in the excitation energy. The variation of the polarization by an external magnetic field depends strongly on the direction of that field. Whereas, the polarization in b-direction increases with an external magnetic field as well in b-direction it can be switched for strong fields in a-direction. The results based on that modified Heisenberg model are in qualitative agreement with experimental data.
Thesberg, Mischa; Sørensen, Erik S
2014-10-22
Ground- and excited-state quantum fidelities in combination with generalized quantum fidelity susceptibilites, obtained from exact diagonalizations, are used to explore the phase diagram of the anisotropic next-nearest-neighbour triangular Heisenberg model. Specifically, the J'-J2 plane of this model, which connects the J1-J2 chain and the anisotropic triangular lattice Heisenberg model, is explored using these quantities. Through the use of a quantum fidelity associated with the first excited-state, in addition to the conventional ground-state fidelity, the BKT-type transition and Majumdar-Ghosh point of the J1-J2 chain (J'=0) are found to extend into the J'-J2 plane and connect with points on the J2=0 axis thereby forming bounded regions in the phase diagram. These bounded regions are then explored through the generalized quantum fidelity susceptibilities χρ, χ₁₂₀°, χD and χCAF which are associated with the spin stiffness, 120° spiral order parameter, dimer order parameter and collinear antiferromagnetic order parameter respectively. These quantities are believed to be extremely sensitive to the underlying phase and are thus well suited for finite-size studies. Analysis of the fidelity susceptibilities suggests that the J', J2≪J phase of the anisotropic triangular model is either a collinear antiferromagnet or possibly a gapless disordered phase that is directly connected to the Luttinger phase of the J1-J2 chain. Furthermore, the outer region is dominated by incommensurate spiral physics as well as dimer order.
Frustration-induced quantum phases in mixed spin chain with frustrated side chains
Hida, Kazuo; Takano, Ken'Ichi
2008-08-01
A mixed Heisenberg spin chain with frustrated side chains is investigated by numerical and perturbational calculations. A frustration-induced quantum partially polarized ferrimagnetic phase and a nonmagnetic spin quadrupolar phase are found adjacent to the conventional Lieb-Mattis-type ferrimagnetic phase or the nonmagnetic singlet cluster solid phases. The partially polarized ferrimagnetic phase has an incommensurate spin structure. Similar structures are commonly found in other frustration-induced partially polarized ferrimagnetic phases. Numerical results also suggest a series of almost critical nonmagnetic ground states in a highly frustrated regime if the side chain spins weakly couple to the main chain.
Probabilities on the Heisenberg group limit theorems and Brownian motion
Neuenschwander, Daniel
1996-01-01
The Heisenberg group comes from quantum mechanics and is the simplest non-commutative Lie group. While it belongs to the class of simply connected nilpotent Lie groups, it turns out that its special structure yields many results which (up to now) have not carried over to this larger class. This book is a survey of probabilistic results on the Heisenberg group. The emphasis lies on limit theorems and their relation to Brownian motion. Besides classical probability tools, non-commutative Fourier analysis and functional analysis (operator semigroups) comes in. The book is intended for probabilists and analysts interested in Lie groups, but given the many applications of the Heisenberg group, it will also be useful for theoretical phycisists specialized in quantum mechanics and for engineers.
Heisenberg scaling of imaging resolution by coherent enhancement
McConnell, Robert; Yoder, Theodore J; Bruzewicz, Colin D; Chuang, Isaac L; Chiaverini, John; Sage, Jeremy M
2016-01-01
Classical imaging works by scattering photons from an object to be imaged, and achieves resolution scaling as $1/\\sqrt{t}$, with $t$ the imaging time. By contrast, the laws of quantum mechanics allow one to utilize quantum coherence to obtain imaging resolution that can scale as quickly as $1/t$ -- the so-called "Heisenberg limit." However, ambiguities in the obtained signal often preclude taking full advantage of this quantum enhancement, while imaging techniques designed to be unambiguous often lose this optimal Heisenberg scaling. Here, we demonstrate an imaging technique which combines unambiguous detection of the target with Heisenberg scaling of the resolution. We also demonstrate a binary search algorithm which can efficiently locate a coherent target using the technique, resolving a target trapped ion to within 3% of the $1/e^2$ diameter of the excitation beam.
Heisenberg in the atomic age science and the public sphere
Carson, Cathryn
2010-01-01
The end of the Second World War opened a new era for science in public life. Heisenberg in the Atomic Age explores the transformations of science's public presence in the postwar Federal Republic of Germany. It shows how Heisenberg's philosophical commentaries, circulating in the mass media, secured his role as science's public philosopher, and it reflects on his policy engagements and public political stands, which helped redefine the relationship between science and the state. With deep archival grounding, the book tracks Heisenberg's interactions with intellectuals from Heidegger to Habermas and political leaders from Adenauer to Brandt. It also traces his evolving statements about his wartime research on nuclear fission for the National Socialist regime. Working between the history of science and German history, the book's central theme is the place of scientific rationality in public life - after the atomic bomb, in the wake of the Third Reich.
Integrable quantum spin chains and their classical continuous counterparts
Avan, Jean; Sfetsos, Konstadinos
2011-01-01
We present certain classical continuum long wave-length limits of prototype integrable quantum spin chains, and define the corresponding construction of classical continuum Lax operators. We also provide two specific examples, i.e. the isotropic and anisotropic Heisenberg models.
Strečka, Jozef; Alécio, Raphael Cavalcante; Lyra, Marcelo L.; Rojas, Onofre
2016-07-01
The spin-1/2 Ising-Heisenberg three-leg tube composed of the Heisenberg spin triangles mutually coupled through the Ising inter-triangle interaction is exactly solved in a zero magnetic field. By making use of the local conservation for the total spin on each Heisenberg spin triangle the model can be rigorously mapped onto a classical composite spin-chain model, which is subsequently exactly treated through the transfer-matrix method. The ground-state phase diagram, correlation functions, concurrence, Bell function, entropy and specific heat are examined in detail. It is shown that the spin frustration represents an indispensable ground for a thermal entanglement, which is quantified by the quantum concurrence. The specific heat displays diverse temperature dependences, which may include a sharp low-temperature peak mimicking a temperature-driven first-order phase transition. It is convincingly evidenced that this anomalous peak originates from massive thermal excitations from the doubly degenerate ground state towards an excited state with a high macroscopic degeneracy due to chiral degrees of freedom of the Heisenberg spin triangles.
Quasi-Linear Algebras and Integrability (the Heisenberg Picture
Directory of Open Access Journals (Sweden)
Alexei Zhedanov
2008-02-01
Full Text Available We study Poisson and operator algebras with the ''quasi-linear property'' from the Heisenberg picture point of view. This means that there exists a set of one-parameter groups yielding an explicit expression of dynamical variables (operators as functions of ''time'' t. We show that many algebras with nonlinear commutation relations such as the Askey-Wilson, q-Dolan-Grady and others satisfy this property. This provides one more (explicit Heisenberg evolution interpretation of the corresponding integrable systems.
XYZ quantum Heisenberg models with p-orbital bosons.
Pinheiro, Fernanda; Bruun, Georg M; Martikainen, Jani-Petri; Larson, Jonas
2013-11-15
We demonstrate how the spin-1/2 XYZ quantum Heisenberg model can be realized with bosonic atoms loaded in the p band of an optical lattice in the Mott regime. The combination of Bose statistics and the symmetry of the p-orbital wave functions leads to a nonintegrable Heisenberg model with antiferromagnetic couplings. Moreover, the sign and relative strength of the couplings characterizing the model are shown to be experimentally tunable. We display the rich phase diagram in the one-dimensional case and discuss finite size effects relevant for trapped systems. Finally, experimental issues related to preparation, manipulation, detection, and imperfections are considered.
Stochastic Heisenberg limit: optimal estimation of a fluctuating phase.
Berry, Dominic W; Hall, Michael J W; Wiseman, Howard M
2013-09-13
The ultimate limits to estimating a fluctuating phase imposed on an optical beam can be found using the recently derived continuous quantum Cramér-Rao bound. For Gaussian stationary statistics, and a phase spectrum scaling asymptotically as ω(-p) with p>1, the minimum mean-square error in any (single-time) phase estimate scales as N(-2(p-1)/(p+1)), where N is the photon flux. This gives the usual Heisenberg limit for a constant phase (as the limit p→∞) and provides a stochastic Heisenberg limit for fluctuating phases. For p=2 (Brownian motion), this limit can be attained by phase tracking.
Characterizations of Sobolev spaces in Euclidean spaces and Heisenberg groups
Institute of Scientific and Technical Information of China (English)
CUI Xiao-yue; LAM Nguyen; LU Guo-zhen
2013-01-01
Recently, many new features of Sobolev spaces W k,p ?RN ? were studied in [4-6, 32]. This paper is devoted to giving a brief review of some known characterizations of Sobolev spaces in Euclidean spaces and describing our recent study of new characterizations of Sobolev spaces on both Heisenberg groups and Euclidean spaces obtained in [12] and [13] and outlining their proofs. Our results extend those characterizations of first order Sobolev spaces in [32] to the Heisenberg group setting. Moreover, our theorems also provide diff erent characterizations for the second order Sobolev spaces in Euclidean spaces from those in [4, 5].
The Path Integral Quantization corresponding to the Deformed Heisenberg Algebra
Pramanik, Souvik; Moussa, Mohamed; Ali, Ahmed Farag
2014-01-01
In this paper, we analyze a deformation of the Heisenberg algebra consistent with both the generalized uncertainty principle and doubly special relativity. We observe that this algebra can give rise to fractional derivatives terms in the corresponding quantum mechanical Hamiltonian. However, a formal meaning can be given to such fractional derivative terms, using the theory of harmonic extensions of functions. Thus we obtain the expression of the propagator of path integral corresponding to this deformed Heisenberg algebra. In fact, we explicitly evaluate this expression for a free particle in one dimension and check its consistency.
Heisenberg-scaled magnetometer with dipolar spin-1 condensates
Xing, Haijun; Wang, Anbang; Tan, Qing-Shou; Zhang, Wenxian; Yi, Su
2016-04-01
We propose a scheme to realize a Heisenberg-scaled magnetometer using dipolar spin-1 condensates. The input state of magnetometer is prepared by slowly sweeping a transverse magnetic field to zero, which yields a highly entangled spin state of N atoms. We show that this process is protected by a parity symmetry such that the state preparation time is within the reach of the current experiment. We also propose a parity measurement with a Stern-Gerlach apparatus which is shown to approach the optimal measurement in the large atom number limit. Finally, we show that the phase estimation sensitivity of the proposed scheme roughly follows the Heisenberg scaling.
The Finite Heisenberg-Weyl Groups in Radar and Communications
Directory of Open Access Journals (Sweden)
Calderbank AR
2006-01-01
Full Text Available We investigate the theory of the finite Heisenberg-Weyl group in relation to the development of adaptive radar and to the construction of spreading sequences and error-correcting codes in communications. We contend that this group can form the basis for the representation of the radar environment in terms of operators on the space of waveforms. We also demonstrate, following recent developments in the theory of error-correcting codes, that the finite Heisenberg-Weyl groups provide a unified basis for the construction of useful waveforms/sequences for radar, communications, and the theory of error-correcting codes.
Institute of Scientific and Technical Information of China (English)
YAO Xiao-yan; LI Peng-lei; DONG Shuai; LIU Jun-ming
2007-01-01
A three-dimensional Ising-like model doped with anti-ferromagnetic (AFM) bonds is proposed to investigate the magnetic properties of a doped triangular spin-chain system by using a Monte-Carlo simulation. The simulated results indicate that a steplike magnetization behavior is very sensitive to the concentration of AFM bonds. A low concentration of AFM bonds can suppress the stepwise behavior considerably, in accordance with doping experiments on Ca3Co206. The analysis of spin snapshots demonstrates that the AFM bond doping not only breaks the ferromagnetic ordered linear spin chains along the hexagonal c-axis but also has a great influence upon the spin configuration in the ab-plane.
Controllability of Linear Systems on Generalized Heisenberg Groups
Dath, Mouhamadou; Jouan, Philippe
2015-01-01
This paper is devoted to the study of controllability of linear systems on generalized Heisenberg groups. Some general necessary controllability conditions and some sufficient ones are provided. We introduce the notion of decoupled systems, and more precise controllability criteria are stated for them.
IMPROVED GAGLIARDO-NIRENBERG INEQUALITIES ON HEISENBERG TYPE GROUPS
Institute of Scientific and Technical Information of China (English)
Luo Guangzhou
2011-01-01
Motivated by the idea of M.Ledoux who brings out the connection between Sobolev embeddings and heat kernel bounds,we prove an analogous result for Kohn's sub-Laplacian on the Heisenberg type groups.The main result includes features of an inequality of either Sobolev or Galiardo-Nirenberg type.
A CARLEMAN ESTIMATE ON GROUPS OF HEISENBERG TYPE
Institute of Scientific and Technical Information of China (English)
Han Junqiang; Niu Pengcheng
2006-01-01
A Pohozaev-Rellich type identity for the p-sub-Laplacian on groups of Heisenberg type, G, is given. A Carleman estimate for the sub-Laplacian on G is established and, as a consequence, a unique continuation result is proved.
Thermodynamics of the Heisenberg ferromagnet in an applied magnetic field.
Flax, L.
1972-01-01
The anisotropic-Heisenberg-ferromagnet formalism developed previously is examined to include an applied magnetic field for the isotropic case in the random-phase approximation. Thermodynamic quantities such as magnetization, susceptibility, and the derivative of magnetization with respect to temperature are studied near the Curie point.
Non-local elliptic systems on the Heisenberg group
Directory of Open Access Journals (Sweden)
Nasser Al-Salti
2016-01-01
Full Text Available We present Liouville type results for certain systems of nonlinear elliptic equations containing fractional powers of the Laplacian on the Heisenberg group. Our method of proof is based on the test function method and a recent inequality proved by Alsaedi, Ahmad, and Kirane, leading to the derivation of sufficient conditions in terms of space dimension and systems parameters.
Hysteresis behavior of the anisotropic quantum Heisenberg model
Energy Technology Data Exchange (ETDEWEB)
Akıncı, Ümit, E-mail: umit.akinci@deu.edu.tr
2013-10-15
The effect of the anisotropy in the exchange interaction on the hysteresis loops within the anisotropic quantum Heisenberg model has been investigated with the effective field theory for two spin cluster. Particular attention has been devoted on the behavior of the hysteresis loop area, coercive field and remanent magnetization with the anisotropy in the exchange interaction for both ferromagnetic and paramagnetic phases.
Entanglement Transfer in a Four-Qubit Dimerized Heisenberg System
Institute of Scientific and Technical Information of China (English)
SHAO Bin; HUANG Min; WANG Zhao-ming; ZOU Jian
2008-01-01
Entanglement transfer is investigated in a dimerized Heisenberg system.Coneurrence as the measure of entanglement is calculated by the time-evolved state starting from an initially entangled state of spin pair.It is shown that perfect entanglement transfer can be realized at 80me special time and suitable interacting.
Slave-Fermion Mean-Field Theory of Heisenberg Model
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
A nearly half-filled two-dimensional Heisenberg model is investigated. A slave-fermion method with fermions as the charge carriers and bosons as the spin carriers is proposed. The ground state shows antiferromagnetic long range order at T = 0. The spin-spin correlation and static susceptibility are also obtained.
Cascade algorithm and multiresolution analysis on the Heisenberg group
Institute of Scientific and Technical Information of China (English)
LIU Heping; LIU Yu; PENG Lizhong; CHU Xiaoyong
2005-01-01
In this paper we investigate the relationship between the convergence of cascade algorithm and orthogonal (or biorthogonal) multiresolution analysis on the Heisenberg group. It is proved that the (strong) convergence of cascade algorithm together with the perfect reconstruction condition induces an orthogonal multiresolution analysis and vice versa. Similar results are also proved for biorthogonal multiresolution analysis.
Entanglement in spin-1/2 dimerized Heisenberg systems
Sun, Z; Hu, A Z; Li, Y Q; Sun, Zhe; Wang, XiaoGuang; Hu, AnZi; Li, You-Quan
2005-01-01
We study entanglement in dimerized Heisenberg systems. In particular, we give exact results of ground-state pairwise entanglement for the four-qubit model by identifying a Z_2 symmetry. Although the entanglements cannot identify the critical point of the system, the mean entanglement of nearest-neighbor qubits really does, namely, it reaches a maximum at the critical point.
Entanglement in Spin-1/2 Dimerized Heisenberg Systems
Institute of Scientific and Technical Information of China (English)
SUN Zhe; WANG Xiao-Guang; HU An-Zi; LI You-Quan
2005-01-01
We study entanglement in dimerized Heisenberg systems. In particular, we give exact results of groundstate pairwise entanglement for the four-qubit model by identifying a Z2 symmetry. Although the entanglements cannot identify the critical point of the system, the mean entanglement of the nearest-neighbor qubits really does, namely, it reaches a maximum at the critical point.
Magnetization direction in the Heisenberg model exhibiting fractional Brownian motion
DEFF Research Database (Denmark)
Zhang, Zhengping; Mouritsen, Ole G.; Zuckermann, Martin J.
1993-01-01
The temporal magnetization-direction fluctuations in the three-dimensional classical ferromagnetic Heisenberg model have been generated by Monte Carlo simulation and analyzed by the rescaled-range method to yield the Hurst exponent H. A value of H congruent-to 1 has been found to apply...
Resolvent kernel for the Kohn Laplacian on Heisenberg groups
Directory of Open Access Journals (Sweden)
Neur Eddine Askour
2002-07-01
Full Text Available We present a formula that relates the Kohn Laplacian on Heisenberg groups and the magnetic Laplacian. Then we obtain the resolvent kernel for the Kohn Laplacian and find its spectral density. We conclude by obtaining the Green kernel for fractional powers of the Kohn Laplacian.
A Poisson type formula for Hardy classes on Heisenberg's group
Directory of Open Access Journals (Sweden)
Lopushansky O.V.
2010-06-01
Full Text Available The Hardy type class of complex functions with infinite many variables defined on the Schrodinger irreducible unitary orbit of reduced Heisenberg group, generated by the Gauss density, is investigated. A Poisson integral type formula for their analytic extensions on an open ball is established. Taylor coefficients for analytic extensions are described by the associatedsymmetric Fock space.
The Bohr-Heisenberg correspondence principle viewed from phase space
DEFF Research Database (Denmark)
Dahl, Jens Peder
2002-01-01
Phase-space representations play an increasingly important role in several branches of physics. Here, we review the author's studies of the Bohr-Heisenberg correspondence principle within the Weyl-Wigner phase-space representation. The analysis leads to refined correspondence rules that can...
Rufo, Sabrina; Mendonça, Griffith; Plascak, J A; de Sousa, J Ricardo
2013-09-01
The ground-state properties of the quasi-one-dimensional spin-1/2 antiferromagnetic Heisenberg model is investigated by using a variational method. Spins on chains along the x direction are antiferromagnetically coupled with exchange J>0, while spins between chains in the y direction are coupled either ferromagnetically (J' 0). The staggered and the colinear antiferromagnetic magnetizations are computed and their dependence on the anisotropy parameter λ=|J'|/J is analyzed. It is found that an infinitesimal interchain coupling parameter is sufficient to stabilize a long-range order with either a staggered magnetization m_{s} (J' > 0) or a colinear antiferromagnetic magnetization m_{caf} (J' < 0), both behaving as ≃λ¹/² for λ → 0.
Heisenberg picture approach to the stability of quantum Markov systems
Energy Technology Data Exchange (ETDEWEB)
Pan, Yu, E-mail: yu.pan@anu.edu.au, E-mail: zibo.miao@anu.edu.au; Miao, Zibo, E-mail: yu.pan@anu.edu.au, E-mail: zibo.miao@anu.edu.au [Research School of Engineering, Australian National University, Canberra, ACT 0200 (Australia); Amini, Hadis, E-mail: nhamini@stanford.edu [Edward L. Ginzton Laboratory, Stanford University, Stanford, California 94305 (United States); Gough, John, E-mail: jug@aber.ac.uk [Institute of Mathematics and Physics, Aberystwyth University, SY23 3BZ Wales (United Kingdom); Ugrinovskii, Valery, E-mail: v.ugrinovskii@gmail.com [School of Engineering and Information Technology, University of New South Wales at ADFA, Canberra, ACT 2600 (Australia); James, Matthew R., E-mail: matthew.james@anu.edu.au [ARC Centre for Quantum Computation and Communication Technology, Research School of Engineering, Australian National University, Canberra, ACT 0200 (Australia)
2014-06-15
Quantum Markovian systems, modeled as unitary dilations in the quantum stochastic calculus of Hudson and Parthasarathy, have become standard in current quantum technological applications. This paper investigates the stability theory of such systems. Lyapunov-type conditions in the Heisenberg picture are derived in order to stabilize the evolution of system operators as well as the underlying dynamics of the quantum states. In particular, using the quantum Markov semigroup associated with this quantum stochastic differential equation, we derive sufficient conditions for the existence and stability of a unique and faithful invariant quantum state. Furthermore, this paper proves the quantum invariance principle, which extends the LaSalle invariance principle to quantum systems in the Heisenberg picture. These results are formulated in terms of algebraic constraints suitable for engineering quantum systems that are used in coherent feedback networks.
Path integral quantization corresponding to the deformed Heisenberg algebra
Energy Technology Data Exchange (ETDEWEB)
Pramanik, Souvik, E-mail: souvick.in@gmail.com [Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata 700108 (India); Moussa, Mohamed, E-mail: mohamed.ibrahim@fsc.bu.edu.eg [Department of Physics, Faculty of Sciences, Benha University, Benha 13518 (Egypt); Faizal, Mir, E-mail: f2mir@uwaterloo.ca [Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, N2L 3G1 (Canada); Ali, Ahmed Farag, E-mail: ahmed.ali@fsc.bu.edu.eg [Department of Physics, Faculty of Sciences, Benha University, Benha 13518 (Egypt)
2015-11-15
In this paper, the deformation of the Heisenberg algebra, consistent with both the generalized uncertainty principle and doubly special relativity, has been analyzed. It has been observed that, though this algebra can give rise to fractional derivative terms in the corresponding quantum mechanical Hamiltonian, a formal meaning can be given to them by using the theory of harmonic extensions of function. Depending on this argument, the expression of the propagator of the path integral corresponding to the deformed Heisenberg algebra, has been obtained. In particular, the consistent expression of the one dimensional free particle propagator has been evaluated explicitly. With this propagator in hand, it has been shown that, even in free particle case, normal generalized uncertainty principle and doubly special relativity show very much different result.
Far-from-equilibrium spin transport in Heisenberg quantum magnets.
Hild, Sebastian; Fukuhara, Takeshi; Schauß, Peter; Zeiher, Johannes; Knap, Michael; Demler, Eugene; Bloch, Immanuel; Gross, Christian
2014-10-03
We study experimentally the far-from-equilibrium dynamics in ferromagnetic Heisenberg quantum magnets realized with ultracold atoms in an optical lattice. After controlled imprinting of a spin spiral pattern with an adjustable wave vector, we measure the decay of the initial spin correlations through single-site resolved detection. On the experimentally accessible time scale of several exchange times, we find a profound dependence of the decay rate on the wave vector. In one-dimensional systems, we observe diffusionlike spin transport with a dimensionless diffusion coefficient of 0.22(1). We show how this behavior emerges from the microscopic properties of the closed quantum system. In contrast to the one-dimensional case, our transport measurements for two-dimensional Heisenberg systems indicate anomalous superdiffusion.
Approaching the Heisenberg Limit without Single-Particle Detection.
Davis, Emily; Bentsen, Gregory; Schleier-Smith, Monika
2016-02-05
We propose an approach to quantum phase estimation that can attain precision near the Heisenberg limit without requiring single-particle-resolved state detection. We show that the "one-axis twisting" interaction, well known for generating spin squeezing in atomic ensembles, can also amplify the output signal of an entanglement-enhanced interferometer to facilitate readout. Applying this interaction-based readout to oversqueezed, non-Gaussian states yields a Heisenberg scaling in phase sensitivity, which persists in the presence of detection noise as large as the quantum projection noise of an unentangled ensemble. Even in dissipative implementations-e.g., employing light-mediated interactions in an optical cavity or Rydberg dressing-the method significantly relaxes the detection resolution required for spectroscopy beyond the standard quantum limit.
Probing quantum discord in a Heisenberg dimer compound.
Chakraborty, Tanmoy; Singh, Harkirat; Singh, Sourabh; Gopal, Radha Krishna; Mitra, Chiranjib
2013-10-23
A quantitative estimation of quantum discord is performed for a Heisenberg spin 1/2 dimer compound (NH4CuPO4, H2O) by means of experimental magnetic and thermal measurements. Magnetic susceptibility and specific heat data were collected for NH4CuPO4, H2O and analyzed within the framework of the Heisenberg isolated dimer model. Internal energy as a function of temperature is obtained by integrating the specific heat versus temperature data. Subsequently, quantum discord, total correlations and spin-spin correlation function are quantified from susceptibility and internal energy and plotted as a function of temperature. Violation of Bell's inequality is also tested for NH4CuPO4, H2O via both experimental susceptibility and specific heat data signifying the presence of entanglement.
Einstein-Euler-Heisenberg Theory and Charged Black Holes
Ruffini, Remo; Xue, She-Sheng
2013-01-01
Taking into account the Euler-Heisenberg effective Lagrangian of one-loop nonperturbative Quantum Electrodynamics (QED) contributions, we formulate the Einstein-Euler-Heisenberg theory, and study the solutions of non-rotating black holes with electric and magnetic charges in spherical geometry. In the limit of strong and weak electromagnetic fields of black holes, we calculate the black hole horizon radius, area, and total energy up to the leading order of QED corrections, and discuss the black hole irreducible mass, entropy, and maximally extractable energy as well as the Christodoulou-Ruffini mass formula. We find that these black hole quantities receive the QED corrections, in comparison with their counterparts in the Reissner-Nortstr\\"om solution. The QED corrections show the screening effect on black hole electric charges and the paramagnetic effect on black hole magnetic charges. As a result, the black hole horizon area, irreducible mass, and entropy increase, however the black hole total energy and max...
Influence of the Heisenberg Principle on the Ideal Bose Gas
Zheng, Hua; Bonasera, Aldo
2013-01-01
The ideal Bose gas has two major shortcomings: at zero temperature, all the particles 'condense' at zero energy or momentum, thus violating the Heisenberg principle; the second is that the pressure below the critical point is independent of density resulting in zero incompressibility (or infinite isothermal compressibility) which is unphysical. We propose a modification of the ideal Bose gas to take into account the Heisenberg principle. This modification results in a finite (in)compressibility at all temperatures and densities. The main properties of the ideal Bose gas are preserved, i.e. the relation between the critical temperature and density, but the specific heat has a maximum at the critical temperature instead of a discontinuity. Of course interactions are crucial for both cases in order to describe actual physical systems.
Euler-Heisenberg-Weiss action for QCD+QED
Ozaki, Sho; Hattori, Koichi; Itakura, Kazunori
2015-01-01
We derive an analytic expression for one-loop effective action of QCD+QED at zero and finite temperatures by using the Schwinger's proper time method. The result is a nonlinear effective action not only for electromagnetic and chromo-electromagnetic fields but also the Polyakov loop, and thus reproduces the Euler-Heisenberg action in QED, QCD, and QED+QCD, and also the Weiss potential for the Polyakov loop at finite temperature. As applications of this "Euler-Heisenberg-Weiss" action in QCD+QED, we investigate quark pair productions induced by QCD+QED fields at zero temperature and the Polyakov loop in the presence of strong electromagnetic fields. Quark one-loop contribution to the effective potential of the Polyakov loop explicitly breaks the center symmetry, and is found to be enhanced by the magnetic field, which is consistent with the inverse magnetic catalysis observed in lattice QCD simulation.
Radiation emission as a virtually exact realization of Heisenbergs microscope
Energy Technology Data Exchange (ETDEWEB)
Andersen, K.K., E-mail: kka@phys.au.dk [Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus C (Denmark); Brock, S. [Department of Culture and Society, Aarhus University, Jens Chr. Skous Vej 5, 8000 Aarhus C (Denmark); Esberg, J.; Thomsen, H.D.; Uggerhøj, U.I. [Department of Physics and Astronomy, Aarhus University, Ny Munkegade 120, 8000 Aarhus C (Denmark)
2013-11-15
Through the concept of ‘formation length’, recently observed directly in the radiation emission from ultrarelativistic electrons and an essential component in the interpretation of strong field radiation from electrons penetrating single crystals, we discuss the indeterminacy in the location of radiation emission. The analogy with the indeterminacy in the Heisenberg microscope Gedanken experiment is demonstrated from a number of viewpoints to be almost exact. The positive attitude regarding photon emission as a process that is somehow located in space and time is emphasized. We therefore interpret the measurements of formation lengths in radiation emission as a practically realizable version – using virtual incident photons instead of real – of the Heisenberg microscope Gedanken experiment.
Laguerre calculus and Paneitz operator on the Heisenberg group
Institute of Scientific and Technical Information of China (English)
CHANG; Der-Chen
2009-01-01
Laguerre calculus is a powerful tool for harmonic analysis on the Heisenberg group.Many sub-elliptic partial differential operators can be inverted by Laguerre calculus.In this article,we use Laguerre calculus to find explicit kernels of the fundamental solution for the Paneitz operator and its heat equation.The Paneitz operator which plays an important role in CR geometry can be written as follows:Here{Zj}n j=1 is an orthonormal basis for the subbundle T(1,0)of the complex tangent bundle TC(Hn) and T is the"missing direction".The operator Lα is the sub-Laplacian on the Heisenberg group which is sub-elliptic ifαdoes not belong to an exceptional setΛα.We also construct projection operators and relative fundamental solution for the operator Lα whileα∈Λα.
Space Group Symmetry Fractionalization in a Chiral Kagome Heisenberg Antiferromagnet.
Zaletel, Michael P; Zhu, Zhenyue; Lu, Yuan-Ming; Vishwanath, Ashvin; White, Steven R
2016-05-13
The anyonic excitations of a spin liquid can feature fractional quantum numbers under space group symmetries. Detecting these fractional quantum numbers, which are analogs of the fractional charge of Laughlin quasiparticles, may prove easier than the direct observation of anyonic braiding and statistics. Motivated by the recent numerical discovery of spin-liquid phases in the kagome Heisenberg antiferromagnet, we theoretically predict the pattern of space group symmetry fractionalization in the kagome lattice SO(3)-symmetric chiral spin liquid. We provide a method to detect these fractional quantum numbers in finite-size numerics which is simple to implement in the density matrix renormalization group. Applying these developments to the chiral spin liquid phase of a kagome Heisenberg model, we find perfect agreement between our theoretical prediction and numerical observations.
Exact solution of the $D_3$ non-Abelian anyon chain
Braylovskaya, Natalia; Frahm, Holger
2016-01-01
Commuting transfer matrices for linear chains of interacting non-Abelian anyons from the two-dimensional irreducible representation of the dihedral group $D_3$ (or, equivalently, the integer sector of the $su(2)_4$ spin-$1$ chain) are constructed using the spin-anyon correspondence to a $D_3$-symmetric formulation of the XXZ Heisenberg spin chain. The spectral problem is solved using discrete inversion identities satisfied by these transfer matrices and functional Bethe ansatz methods. The resulting spectrum can be related to that of the XXZ spin-$1/2$ Heisenberg chain with boundary conditions depending on the topological sector of the anyon chain. The properties of this model in the critical regime are studied by finite size analysis of the spectrum. In particular, points in the phase diagram where the anyon chain realizes some of the rational $\\mathbb{Z}_2$ orbifold theories are identified.
Exact solution of the D3 non-Abelian anyon chain
Braylovskaya, Natalia; Finch, Peter E.; Frahm, Holger
2016-08-01
Commuting transfer matrices for linear chains of interacting non-Abelian anyons from the two-dimensional irreducible representation of the dihedral group D3 [or, equivalently, the integer sector of the s u (2) 4 spin-1 chain] are constructed using the spin-anyon correspondence to a D3-symmetric formulation of the XXZ Heisenberg spin chain. The spectral problem is solved using discrete inversion identities satisfied by these transfer matrices and functional Bethe ansatz methods. The resulting spectrum can be related to that of the XXZ spin-1/2 Heisenberg chain with boundary conditions depending on the topological sector of the anyon chain. The properties of this model in the critical regime are studied by finite size analysis of the spectrum. In particular, points in the phase diagram where the anyon chain realizes some of the rational Z2 orbifold theories are identified.
Institute of Scientific and Technical Information of China (English)
Jing Wen LUAN; Fu Liu ZHU
2005-01-01
In this paper, we make the asymptotic estimates of the heat kernel for the quaternionic Heisenberg group in various cases. We also use these results to deduce the asymptotic estimates of certain harmonic functions on the quaternionic Heisenberg group. Moreover a Martin compactification of the quaternionic Heisenberg group is constructed, and we prove that the Martin boundary of this group is homeomorphic to the unit ball in the quaternionic field.
Uniqueness of a positive solution for quasilinear elliptic equations in Heisenberg group
Directory of Open Access Journals (Sweden)
Kaushik Bal
2016-06-01
Full Text Available In this note we address the question of uniqueness of the Brezis-Oswald problem for the p-Laplacian operator in Heisenberg Group. The non-availability of $C^{1,\\alpha}$ regularity for all $1
Heisenberg Group case. We overcome the problem by proving directly a generalized version of Diaz-Saa inequality in the Heisenberg Group.
[Carl Friedrich von Weizsäcker and Werner Heisenberg].
Cassidy, David C
2014-01-01
The 50-year relationship between Weizsäcker and Heisenberg spanned the highpoints of discovery and dictatorship during the 1930s, extended into the war-time uranium project, the post-war controversy over that project, debates over West German nuclear policy, and the philosophical implications of modern physics. This paper explores the interaction between these two leading figures during that difficult and significant half-century.
Large-scale numerical investigations of the antiferromagnetic Heisenberg icosidodecahedron
Energy Technology Data Exchange (ETDEWEB)
Ummethum, Joerg [Department of Physics, Bielefeld University, P.O. Box 100131, D-33501 Bielefeld (Germany); Schnack, Juergen, E-mail: jschnack@uni-bielefeld.de [Department of Physics, Bielefeld University, P.O. Box 100131, D-33501 Bielefeld (Germany); Laeuchli, Andreas M. [Inst. f. Theoretische Physik, Innsbruck University, Technikerstr. 25, 6020 Innsbruck (Austria)
2013-02-15
We present up to date investigations of the antiferromagnetic Heisenberg icosidodecahedron by means of the density matrix renormalization group method. We compare our results with modern correlator product state as well as Lanczos calculations. - Highlights: Black-Right-Pointing-Pointer Results of unprecedented accuracy for energies and correlation functions of a frustrated spin system. Black-Right-Pointing-Pointer Relevance for a large set of magnetic molecules. Black-Right-Pointing-Pointer Demonstration of accuracy of DDMRG.
Decay of transverse correlations in quantum Heisenberg models
Energy Technology Data Exchange (ETDEWEB)
Björnberg, Jakob E., E-mail: jakob.bjornberg@gmail.com, E-mail: daniel@ueltschi.org [Department of Mathematical Sciences, Chalmers and University of Gothenburg, 41296 Göteborg (Sweden); Ueltschi, Daniel, E-mail: jakob.bjornberg@gmail.com, E-mail: daniel@ueltschi.org [Department of Mathematics, University of Warwick, Coventry CV4 7AL (United Kingdom)
2015-04-15
We study a class of quantum spin systems that include the S=1/2 Heisenberg and XY-models and prove that two-point correlations exhibit exponential decay in the presence of a transverse magnetic field. The field is not necessarily constant, it may be random, and it points in the same direction. Our proof is entirely probabilistic and it relies on a random loop representations of the correlation functions, on stochastic domination and on first-passage percolation.
Inspiration of Heisenberg Uncertainty Principle to College Education
Institute of Scientific and Technical Information of China (English)
梁讯
2008-01-01
No matter how accurately one tried to measure the classical quantities of position and momentum, there would always be an uncertainty in the measurement.The Heisenberg Principle of Uncertainty is one of the most significant changes in our comprehension of the universe, it inspired people once again to think the unthinkable, and challenge the very foundations of subjects in both research and educational fields.
Scaling behavior of the Heisenberg model in three dimensions.
Gordillo-Guerrero, A; Kenna, R; Ruiz-Lorenzo, J J
2013-12-01
We report on extensive numerical simulations of the three-dimensional Heisenberg model and its analysis through finite-size scaling of Lee-Yang zeros. Besides the critical regime, we also investigate scaling in the ferromagnetic phase. We show that, in this case of broken symmetry, the corrections to scaling contain information on the Goldstone modes. We present a comprehensive Lee-Yang analysis, including the density of zeros, and confirm recent numerical estimates for critical exponents.
Spatially frustrated S = 1 Heisenberg antiferromagnet with single ion anisotropy
Pires, A. S. T.
2016-10-01
Using the SU(3) Schwinger boson formalism, I study the S = 1 square lattice Heisenberg antiferromagnet, at zero temperature, with spatially anisotropic nearest-neighbor couplings frustrated by a next-nearest neighbor interaction and single ion anisotropy. The phase diagram at zero temperature is presented. My calculations show two magnetically ordered phases separated by a quantum-disordered region for all values of the anisotropy.
Creation of Multipartite Entanglement and Entanglement Transfer via Heisenberg Interaction
Institute of Scientific and Technical Information of China (English)
ZHANG Yong; CAO Wan-Cang; LONG Gui-Lu
2005-01-01
@@ We discuss how to create multipartite entanglement. By coupling a new particle with entangled particles via Heisenberg interaction between two particles, we can prepare three-particle entangled states. For some special coupling strength, entanglement transfer can be achieved from entangled pair AB to particles A and C that never interact by coupling particle C with particle B, which can be used to create entanglement between two separated particles.
Directory of Open Access Journals (Sweden)
Tetsuo Deguchi
2011-06-01
Full Text Available We show some symmetry relations among the correlation functions of the integrable higher-spin XXX and XXZ spin chains, where we explicitly evaluate the multiple integrals representing the one-point functions in the spin-1 case. We review the multiple-integral representations of correlation functions for the integrable higher-spin XXZ chains derived in a region of the massless regime including the anti-ferromagnetic point. Here we make use of the gauge transformations between the symmetric and asymmetric R-matrices, which correspond to the principal and homogeneous gradings, respectively, and we send the inhomogeneous parameters to the set of complete 2s-strings. We also give a numerical support for the analytical expression of the one-point functions in the spin-1 case.
Modern or Anti-modern Science? Weimar Culture, Natural Science and the Heidegger-Heisenberg Exchange
Carson, Cathryn
The following sections are included: * Weimar Culture and Scientific Rationality * Heidegger Read Historically * Science and Crisis * Quantum Mechanics and the Heidegger-Heisenberg Exchange * Conclusion * Acknowledgments
Random field distributed Heisenberg model on a thin film geometry
Energy Technology Data Exchange (ETDEWEB)
Akıncı, Ümit, E-mail: umit.akinci@deu.edu.tr
2014-11-15
The effects of the bimodal random field distribution on the thermal and magnetic properties of the Heisenberg thin film have been investigated by making use of a two spin cluster with the decoupling approximation. Particular attention has been devoted to the obtaining of phase diagrams and magnetization behaviors. The physical behaviors of special as well as tricritical points are discussed for a wide range of selected Hamiltonian parameters. For example, it is found that when the strength of a magnetic field increases, the locations of the special point (which is the ratio of the surface exchange interaction and the exchange interaction of the inner layers that makes the critical temperature of the film independent of the thickness) in the related plane decrease. Moreover, tricritical behavior has been obtained for higher values of the magnetic field, and influences of the varying Hamiltonian parameters on its behavior have been elucidated in detail in order to have a better understanding of the mechanism underlying the considered system. - Highlights: • Effect of bimodal random field distribution within the Heisenberg model is investigated. • Phase diagrams of the random field Heisenberg model in a thin film geometry are obtained. • Effect of the random field on the magnetic properties is obtained. • Variation of the special point with random field is determined. • Variation of the tricritical point with random field is determined.
Global phase diagram of a doped Kitaev-Heisenberg model
Energy Technology Data Exchange (ETDEWEB)
Okamoto, Satoshi [ORNL
2013-01-01
The global phase diagram of a doped Kitaev-Heisenberg model is studied using an $SU(2)$ slave-boson mean-field method. Near the Kitaev limit, $p$-wave superconducting states which break the time-reversal symmetry are stabilized as reported by You {\\it et al.} [Phys. Rev. B {\\bf 86}, 085145 (2012)] irrespective of the sign of the Kitaev interaction. By further doping, a $d$-wave superconducting state appears when the Kitaev interaction is antiferromagnetic, while another $p$-wave superconducting state appears when the Kitaev interaction is ferromagnetic. This $p$-wave superconducting state does not break the time-reversal symmetry as reported by Hyart {\\it et al.} [Phys. Rev. B {\\bf 85}, 140510 (2012)], and such a superconducting state also appears when the antiferromagnetic Kitaev interaction and the ferromagnetic Heisenberg interaction compete. This work, thus, demonstrates the clear difference between the antiferromagnetic Kitaev model and the ferromagnetic Kitaev model when carriers are doped while these models are equivalent in the undoped limit, and how novel superconducting states emerge when the Kitaev interaction and the Heisenberg interaction compete.
Strecka, Jozef; Canová, Lucia; Minami, Kazuhiko
2009-05-01
The spin-1/2 Ising-Heisenberg model with the pair XYZ Heisenberg interaction and quartic Ising interactions is exactly solved by establishing a precise mapping relationship with the corresponding zero-field (symmetric) eight-vertex model. It is shown that the Ising-Heisenberg model with the ferromagnetic Heisenberg interaction exhibits a striking critical behavior, which manifests itself through re-entrant phase transitions as well as continuously varying critical exponents. The changes in critical exponents are in accordance with the weak universality hypothesis in spite of a peculiar singular behavior that emerges at a quantum critical point of the infinite order, which occurs at the isotropic limit of the Heisenberg interaction. On the other hand, the Ising-Heisenberg model with the antiferromagnetic Heisenberg interaction surprisingly exhibits less significant changes in both critical temperatures and critical exponents upon varying the strength of the exchange anisotropy in the Heisenberg interaction.
Modified Heisenberg model for the zig-zag structure in multiferroic RMn{sub 2}O{sub 5}
Energy Technology Data Exchange (ETDEWEB)
Bahoosh, Safa Golrokh, E-mail: safa.bahoosh@uni-konstanz.de [Department of Physics, University of Konstanz, D-78457 Konstanz (Germany); Wesselinowa, Julia M., E-mail: julia@phys.uni-sofia.bg [Department of Physics, University of Sofia, 1164 Sofia (Bulgaria); Trimper, Steffen, E-mail: steffen.trimper@physik.uni-halle.de [Institute of Physics, Martin-Luther-University Halle-Wittenberg, D-06099 Halle (Germany)
2015-08-28
The class of RMn{sub 2}O{sub 5} (R = Ho, Tb, Y, Eu) compounds offers multiferroic properties where the refined magnetic zig-zag order breaks the inversion symmetry. Varying the temperature, the system undergoes a magnetic and a subsequent ferroelectric phase transition where the ferroelectricity is magnetically induced. We propose a modified anisotropic Heisenberg model that can be used as a tractable analytical model studying the properties of those antiferromagnetic zig-zag spin chains. Based on a finite temperature Green's function method, it is shown that the polarization is induced solely by different exchange couplings of the two different Mn{sup 4+} and Mn{sup 3+} magnetic ions. We calculate the excitation energy of the spin system for finite temperatures, which for its part determines the temperature dependent magnetization and polarization. The ferroelectric phase transition is manifested as a kink in the excitation energy. The variation of the polarization by an external magnetic field depends strongly on the direction of that field. Whereas, the polarization in b-direction increases with an external magnetic field as well in b-direction it can be switched for strong fields in a-direction. The results based on that modified Heisenberg model are in qualitative agreement with experimental data.
A FUNDAMENTAL SOLUTION FOR THE LAPLACE OPERATOR ON THE QUATERNIONIC HEISENBERG GROUP
Institute of Scientific and Technical Information of China (English)
朱理
2002-01-01
In this paper, the author studies the Laplace operator on the quaternionic Heisenberg group, construct a fundamental solution for it and use this solution to prove the LP-boundedness and the weak (1-1) boundedness of certain singular convolution operators on the quaternionic Heisenberg group.
Analysis of the migdal transformation for models with Heisenberg spins on a d-dimensional lattice
Schoenmaker, B.; Ruijgrok, Th.W.
1988-01-01
We show for classical Heisenberg spins, with a general nearest neighbour interaction, that in the Migdal approximation the only low-temperature phase transitions are Ising ones (ferror antiferromagnetic). For d=2 neither the pure Heisenberg model nor the Lebwohl-Lasher model show a phase transition
BIHARMONIC S-CURVES ACCORDING TO SABBAN FRAME IN HEISENBERG GROUP Heis³
Directory of Open Access Journals (Sweden)
Talat Körpinar
2013-02-01
Full Text Available In this paper, we study biharmonic curves accordig to Sabban frame in the Heisenberg group Heis³. We characterize the biharmonic curves in terms of their geodesic curvature and we prove that all of biharmonic curves are helices in the Heisenberg group Heis³. Finally, we find out their explicit parametric equations according to Sabban Frame.
Weighted Rellich Inequality on H-Type Groups and Nonisotropic Heisenberg Groups
Directory of Open Access Journals (Sweden)
Han Yazhou
2010-01-01
Full Text Available We prove a sharp weighted Rellich inequality associated with a class of Greiner-type vector fields on H-type groups. We also obtain some weighted Hardy- and Rellich-type inequalities on nonisotropic Heisenberg groups. As an application, we get a Rellich-Sobolev-type inequality on Heisenberg groups.
Heisenberg-Type Families in $U_q(widehat{sl_2}$
Directory of Open Access Journals (Sweden)
Alexander Zuevsky
2009-01-01
Full Text Available Using the second Drinfeld formulation of the quantized universal enveloping algebra $U_q(widehat{sl_2}$ we introduce a family of its Heisenberg-type elements which are endowed with a deformed commutator and satisfy properties similar to generators of a Heisenberg subalgebra. Explicit expressions for new family of generators are found.
Yersultanova, Z. S.; Zhassybayeva, M.; Yesmakhanova, K.; Nugmanova, G.; Myrzakulov, R.
2016-10-01
Integrable Heisenberg ferromagnetic equations are an important subclass of integrable systems. The M-XCIX equation is one of a generalizations of the Heisenberg ferromagnetic equation and are integrable. In this paper, the Darboux transformation of the M-XCIX equation is constructed. Using the DT, a 1-soliton solution of the M-XCIX equation is presented.
MULTIRESOLUTION ANALYSIS, SELF-SIMILAR TILINGS AND HAAR WAVELETS ON THE HEISENBERG GROUP
Institute of Scientific and Technical Information of China (English)
Liu Heping; Liu Yu; Wang Haihui
2009-01-01
In this article, the properties of multiresolution analysis and self-similar tilings on the Heisenberg group are studied. Moreover, we establish a theory to construct an orthonormal Haar wavelet base in L~2(H~d) by using self-similar tilings for the acceptable dilations on the Heisenberg group.
An index formula for the extended Heisenberg algebra of Epstein, Melrose and Mendoza
van Erp, Erik
2010-01-01
The extended Heisenberg algebra for a contact manifold contains, as subalgebras, both the Heisenberg algebra as well as the classical pseudodifferential operators. We derive here a formula for the index of Fredholm operators in this extended calculus. This formula incorporates in a single expression the Atiyah-Singer formula for elliptic operators, as well as Boutet de Monvel's Toeplitz index formula.
Heisenberg double of supersymmetric algebras for noncommutative quantum field theory
Kirchanov, V. S.
2013-09-01
The ground work is laid for the construction of a Heisenberg superdouble in the form of a smash product of a standard Poincaré-Lie quantum-operator superalgebra with coalgebra and its double Lie spatial superalgebra with coalgebra, which are Hopf algebras and a Hopf modular algebra, respectively. Deformation of the superalgebras is realized by Drinfeld twists for the shift and supershift operators. As a result, an extended algebra is obtained, containing a non(anti)commutative superspace and quantum-group generators.
A Liouville Theorem for Nonlocal Equations in the Heisenberg Group
Directory of Open Access Journals (Sweden)
Eleonora Cinti
2014-12-01
Full Text Available We establish a Liouville-type theorem for a subcritical nonlinear problem, involving a fractional power of the sub-Laplacian in the Heisenberg group. To prove our result we will use the local realization of fractional CR covariant operators, which can be constructed as the Dirichlet-to-Neumann operator of a degenerate elliptic equation in the spirit of Caffarelli and Silvestre [8], as established in [14]. The main tools in our proof are the CR inversion and the moving plane method, applied to the solution of the lifted problem in the half-space ℍn × ℝ+.
Heisenberg uncertainty relation and statistical measures in the square well
Directory of Open Access Journals (Sweden)
Jaime Sañudo
2012-07-01
Full Text Available A non stationary state in the one-dimensional infinite square well formed by a combination of the ground state and the first excited one is considered. The statistical complexity and the Fisher-Shannon entropy in position and momentum are calculated with time for this system. These measures are compared with the Heisenberg uncertainty relation, $Delta xDelta p$. It is observed that the extreme values of $Delta xDelta p$ coincide in time with extreme values of the other two statistical magnitudes.
Quantification of quantum discord in a antiferromagnetic Heisenberg compound
Energy Technology Data Exchange (ETDEWEB)
Singh, H., E-mail: chiranjib@iiserkol.ac.in; Chakraborty, T., E-mail: chiranjib@iiserkol.ac.in; Mitra, C., E-mail: chiranjib@iiserkol.ac.in [Indian Institute of Science Education and Research (IISER) Kolkata, Mohanpur Campus, Mohanpur -741252, Nadia, West Bengal (India)
2014-04-24
An experimental quantification of concurrence and quantum discord from heat capacity (C{sub p}) measurement performed over a solid state system has been reported. In this work, thermodynamic measurements were performed on copper nitrate (CN, Cu(NO{sub 3}){sub 2}⋅2.5H{sub 2}O) single crystals which is an alternating antiferromagnet Heisenberg spin 1/2 system. CN being a weak dimerized antiferromagnet is an ideal system to investigate correlations between spins. The theoretical expressions were used to obtain concurrence and quantum discord curves as a function of temperature from heat capacity data of a real macroscopic system, CN.
Yang-Lee Circle Theorem for an Antiferromagnetic Heisenberg Ladder
Institute of Scientific and Technical Information of China (English)
王先智
2001-01-01
The Yang-Lee zeros of an antiferromagnetic Heisenberg ladder model are determined. It is found that if J4≤0 Yang-Lee zeros are located on the unit circle and on the negative real axis in the complex activity plane. In particular, if J4≤0 and 2J2≥J4, Yang-Lee zeros are located on the unit circle and the Yang-Lee circle theorem is valid. If J4 ＞ 0, Yang-Lee zeros are located on some complicated curves.
Multicritical point in a diluted bilayer Heisenberg quantum antiferromagnet.
Sandvik, Anders W
2002-10-21
The S=1/2 Heisenberg bilayer antiferromagnet with randomly removed interlayer dimers is studied using quantum Monte Carlo simulations. A zero-temperature multicritical point (p(*),g(*)) at the classical percolation density p=p(*) and interlayer coupling g(*) approximately equal 0.16 is demonstrated. The quantum critical exponents of the percolating cluster are determined using finite-size scaling. It is argued that the associated finite-temperature quantum critical regime extends to zero interlayer coupling and could be relevant for antiferromagnetic cuprates doped with nonmagnetic impurities.
Knight shifts around vacancies in the 2D Heisenberg model.
Anfuso, Fabrizio; Eggert, Sebastian
2006-01-13
The local response to a uniform field around vacancies in the two-dimensional spin-1/2 Heisenberg antiferromagnet is determined by numerical quantum Monte Carlo simulations as a function of temperature. It is possible to separate the Knight shifts into uniform and staggered contributions on the lattice which are analyzed and understood in detail. The contributions show interesting long- and short-range behavior that may be of relevance in NMR and susceptibility measurements. For more than one impurity, remarkable nonlinear enhancement and cancellation effects take place. We predict that the Curie impurity susceptibility will be observable for a random impurity concentration even in the thermodynamic limit.
Ground states of the SU(N) Heisenberg model.
Kawashima, Naoki; Tanabe, Yuta
2007-02-02
The SU(N) Heisenberg model with various single-row representations is investigated by quantum Monte Carlo simulations. While the zero-temperature phase boundary agrees qualitatively with the theoretical predictions based on the 1/N expansion, some unexpected features are also observed. For N> or =5 with the fundamental representation, for example, it is suggested that the ground states possess exact or approximate U(1) degeneracy. In addition, for the representation of Young tableau with more than one column, the ground state shows no valence-bond-solid order even at N greater than the threshold value.
Fluctuation-dissipation ratio of the Heisenberg spin glass.
Kawamura, Hikaru
2003-06-13
The fluctuation-dissipation (FD) relation of the three-dimensional Heisenberg spin glass with weak random anisotropy is studied by off-equilibrium Monte Carlo simulation. The numerically determined FD ratio exhibits a "one-step-like" behavior, the effective temperature of the spin-glass state being about twice the spin-glass transition temperature, T(eff) approximately 2T(g), irrespective of the bath temperature. The results are discussed in conjunction with the recent experiment by Hérisson and Ocio, and with the chirality scenario of the spin-glass transition.
REPLICA ORNSTEIN-ZERNIKE EQUATIONS FOR POSITIONALLY FROZEN HEISENBERG SYSTEMS
Directory of Open Access Journals (Sweden)
E.Lomba
2003-01-01
Full Text Available We present the formulation of the Replica Ornstein-Zernike equations for a model of positionally frozen disordered Heisenberg spin system. The results are obtained for various models, one in which the particle positions correspond to a frozen hard sphere fluid, another system in which the configurations are generated by a random insertion of hard spheres, a system of randomly distributed spins, and finally a system corresponding to a soft sphere fluid quenched at high and low temperatures. We will see that the orientational structure of the spin system is fairly well reproduced by the integral equation which, however, does not correctly account for the critical behaviour.
Some Properties of Quasiconvex Functions on the Heisenberg Group
Institute of Scientific and Technical Information of China (English)
Ming-bao Sun; Xiao-ping Yang
2005-01-01
For the Heisenberg group, we introduce the concept of h-quasiconvex functions. We prove that the notions of h-quasiconvex functions and h-convex set are equivalent and that h-quasiconvex functions are locally bounded from above, and furthermore derive that h-convex functions are locally bounded, therefore it is locally Lipschitz continuous by using recent results by Danielli-Garofalo-Nhieu. Finally we give estimates of the L∞norm of the first derivatives of h-quasiconvex functions.
Origin of the anomalies the modified Heisenberg equation
Estève, J G
2002-01-01
The origin of the anomalies is analyzed. It is shown that they are due to the fact that the generators of the symmetry do not leave invariant the domain of definition of the Hamiltonian and then a term, normally forgotten in the Heisenberg equation, gives an extra contribution responsible for the non conservation of the charges. This explanation is equivalent to that of the Fujikawa in the path integral formalism. Finally, this approach is applied to the conformal symmetry breaking in two-dimensional quantum mechanics.
Superconformal quantum mechanics via Wigner-Heisenberg algebra
Energy Technology Data Exchange (ETDEWEB)
Carrion, H.L. [Centro Brasileiro de Pesquisas Fisicas (CBPF), Rio de Janeiro, RJ (Brazil)]|[Universidade Federal, Rio de Janeiro, RJ (Brazil). Inst. de Fisica; E-mail: hleny@cbpf.br; Rodrigues, R. de Lima [Paraiba Univ., Cajazeiras, PB (Brazil). Dep. de Ciencias Exatas e da Natureza]. E-mail: rafael@df.ufcg.edu.br
2004-03-01
We show the natural relation between the Wigner Hamiltonian and the conformal Hamiltonian. It is presented a model in (super)conformal quantum mechanics with (super)conformal symmetry in the Wigner-Heisenberg algebra picture [x,p{sub x}]=i(1+cP) (P being the parity operator). In this context, the energy spectrum, the Casimir operator, creation and annihilation operators are defined. This superconformal Hamiltonian is similar to the super-Hamiltonian of the Calogero model and it is also an extension of the super-Hamiltonian for the Dirac Oscillator. (author)
Asymptotics of the mean-field Heisenberg model
Kirkpatrick, Kay
2012-01-01
We consider the mean-field classical Heisenberg model and obtain detailed information about the magnetization by studying the model on a complete graph and sending the number of vertices to infinity. In particular, we obtain Cram\\`er- and Sanov-type large deviations principles for the magnetization and the empirical spin distribution and demonstrate a second-order phase transition in the Gibbs measures. We also study the asymptotics of the magnetization throughout the phase transition using Stein's method, proving central limit theorems in the sub- and supercritical phases and a nonnormal limit theorem at the critical temperature.
Hida, Kazuo; Shiino, Masaru; Chen, Wei
2004-06-01
The magnetization plateaux in two dimensionally coupled S=1/2 dimerized zigzag Heisenberg chains are investigated by means of the bond operator mean field approximation. In the absence of the interchain coupling, this model is known to have a plateau at half of the saturation magnetization accompanied by the spontaneous translational symmetry breakdown. The parameter regime in which the plateau appears is reproduced well within the present approximation. In the presence of the interchain coupling, this plateau is shown to be suppressed. This result is also supported by the numerical diagonalization calculation.
Heavy hadron spectra from spin chains and strings
Cotrone, A L; Pons, J M; Talavera, P
2007-01-01
We study the spectrum of hadronic states made up of very massive complex scalar fields in a confining gauge theory admitting a supergravity dual background. We show that for a sub-sector of operators dual to certain spinning strings, the mass spectrum exhibits an integrable structure equal to the Heisenberg spin chain, up to an overall factor. This result is compared with the corresponding string prediction.
Realistic Approach of the Relations of Uncertainty of Heisenberg
Directory of Open Access Journals (Sweden)
Paul E. Sterian
2013-01-01
Full Text Available Due to the requirements of the principle of causality in the theory of relativity, one cannot make a device for the simultaneous measuring of the canonical conjugate variables in the conjugate Fourier spaces. Instead of admitting that a particle’s position and its conjugate momentum cannot be accurately measured at the same time, we consider the only probabilities which can be determined when working at subatomic level to be valid. On the other hand, based on Schwinger's action principle and using the quadridimensional form of the unitary transformation generator function of the quantum operators in the paper, the general form of the evolution equation for these operators is established. In the nonrelativistic case one obtains the Heisenberg's type evolution equations which can be particularized to derive Heisenberg's uncertainty relations. The analysis of the uncertainty relations as implicit evolution equations allows us to put into evidence the intrinsic nature of the correlation expressed by these equations in straight relations with the measuring process. The independence of the quantisation postulate from the causal evolution postulate of quantum mechanics is also put into discussion.
On Hopf algebroid structure of kappa-deformed Heisenberg algebra
Lukierski, Jerzy; Woronowicz, Mariusz
2016-01-01
The $(4+4)$-dimensional $\\kappa$-deformed quantum phase space as well as its $(10+10)$-dimensional covariant extension by the Lorentz sector can be described as Heisenberg doubles: the $(10+10)$-dimensional quantum phase space is the double of $D=4$ $\\kappa$-deformed Poincar\\'e Hopf algebra $\\mathbb{H}$ and the standard $(4+4)$-dimensional space is its subalgebra generated by $\\kappa$-Minkowski coordinates $\\hat{x}_\\mu$ and corresponding commuting momenta $\\hat{p}_\\mu$. Every Heisenberg double appears as the total algebra of a Hopf algebroid over a base algebra which is in our case the coordinate sector. We exhibit the details of this structure, namely the corresponding right bialgebroid and the antipode map. We rely on algebraic methods of calculation in Majid-Ruegg bicrossproduct basis. The target map is derived from a formula by J-H. Lu. The coproduct takes values in the bimodule tensor product over a base, what is expressed as the presence of coproduct gauge freedom.
Laguerre calculus and Paneitz operator on the Heisenberg group
Institute of Scientific and Technical Information of China (English)
CHANG Der-Cheni; CHANG Shu-Cheng; TIE JingZhi
2009-01-01
Laguerre calculus is a powerful tool for harmonic analysis on the Heisenberg group. Many sub-elliptic partial differential operators can be inverted by Laguerre calculus. In this article,we use Laguerre calculus to find explicit kernels of the fundamental solution for the Paneitz operator and its heat equation. The Paneitz operator which plays an important role in CR geometry can be written as follows: Ρ_α=(ν)_a(ν)_a=4/1[∑n/j=1(Z_jZ_j+Z_jZ_j]~2+a~2T~2.Here {Z~j}~n_j=1 is an orthonormal basis for the subbundle T~(1,0) of the complex tangent bundle T_c(H_n) and T is the "missing direction". The operator ν_a is the sub-Laplaeian on the Heisenberg group which is sub-elliptic if α does not belong to an exceptional set Aα. We also construct projection operators and relative fundamental solution for the operator (ν)_α while α∈ (A)_α.
The Heisenberg antiferromagnet on the square-kagomé lattice
Directory of Open Access Journals (Sweden)
J. Richter
2009-01-01
Full Text Available We discuss the ground state, the low-lying excitations as well as high-field thermodynamics of the Heisenberg antiferromagnet on the two-dimensional square-kagomé lattice. This magnetic system belongs to the class of highly frustrated spin systems with an infinite non-trivial degeneracy of the classical ground state as it is also known for the Heisenberg antiferromagnet on the kagomé and on the star lattice. The quantum ground state of the spin-half system is a quantum paramagnet with a finite spin gap and with a large number of non-magnetic excitations within this gap. We also discuss the magnetization versus field curve that shows a plateaux as well as a macroscopic magnetization jump to saturation due to independent localized magnon states. These localized states are highly degenerate and lead to interesting features in the low-temperature thermodynamics at high magnetic fields such as an additional low-temperature peak in the specific heat and an enhanced magnetocaloric effect.
Linearized pseudo-Einstein equations on the Heisenberg group
Barletta, Elisabetta; Dragomir, Sorin; Jacobowitz, Howard
2017-02-01
We study the pseudo-Einstein equation R11bar = 0 on the Heisenberg group H1 = C × R. We consider first order perturbations θɛ =θ0 + ɛ θ and linearize the pseudo-Einstein equation about θ0 (the canonical Tanaka-Webster flat contact form on H1 thought of as a strictly pseudoconvex CR manifold). If θ =e2uθ0 the linearized pseudo-Einstein equation is Δb u - 4 | Lu|2 = 0 where Δb is the sublaplacian of (H1 ,θ0) and L bar is the Lewy operator. We solve the linearized pseudo-Einstein equation on a bounded domain Ω ⊂H1 by applying subelliptic theory i.e. existence and regularity results for weak subelliptic harmonic maps. We determine a solution u to the linearized pseudo-Einstein equation, possessing Heisenberg spherical symmetry, and such that u(x) → - ∞ as | x | → + ∞.
Chiral spin liquid in a frustrated anisotropic kagome Heisenberg model.
He, Yin-Chen; Sheng, D N; Chen, Yan
2014-04-04
Kalmeyer-Laughlin (KL) chiral spin liquid (CSL) is a type of quantum spin liquid without time-reversal symmetry, and it is considered as the parent state of an exotic type of superconductor--anyon superconductor. Such an exotic state has been sought for more than twenty years; however, it remains unclear whether it can exist in a realistic system where time-reversal symmetry is breaking (T breaking) spontaneously. By using the density matrix renormalization group, we show that KL CSL exists in a frustrated anisotropic kagome Heisenberg model, which has spontaneous T breaking. We find that our model has two topological degenerate ground states, which exhibit nonvanishing scalar chirality order and are protected by finite excitation gap. Furthermore, we identify this state as KL CSL by the characteristic edge conformal field theory from the entanglement spectrum and the quasiparticles braiding statistics extracted from the modular matrix. We also study how this CSL phase evolves as the system approaches the nearest-neighbor kagome Heisenberg model.
High Field Magnetization Studies of Low Dimensional Heisenberg S = 1/2 Antiferromagnets
Landee, C. P.; Turnbull, M. M.
1998-03-01
The magnetization curves of a number of low dimensional S=1/2 Heisenberg antiferromagnets have been determined in fields up to 30 tesla at low temperatures at the National High Magnetic Fields Laboratory. Materials studied include a family of 1D materials, based upon Cu(pyrazine)(NO_3)_2, 2D magnets consisting of pyrazine-bridged copper layers, and several spin ladders with singlet ground states. All of the magnetization data show upward curvature and are well described by T = 0 calculations based upon finite cluster models(Bonner and Fisher, Phys. Rev. A135, 640 (1964); Yang and Mutter, NANL cond-mat/9610092.). Chemical substitution on the pyrazine rings permits the variation of exchange constants by more than 25 percent for the family of well isolated chains. The spin ladder systems consist of ferromagnetic dimers weakly connected by antiferromagnetic intradimer interactions. Field induced transitions are seen at fields of less than one tesla for each of the three compounds.
Boukahil, A.; Huber, D. L.
1989-09-01
The harmonic magnon modes in a one-dimensional Heisenberg spin glass having nearest-neighbor exchange interactions of fixed magnitude and random sign are investigated. The Lyapounov exponent is calculated for chains of 107-108 spins over the interval 0<=ω<=4J. In the low-frequency regime, ω<~0.1J, an anomalous behavior for the density of states ρ(ω)~ω-1/3 is established, consistent with earlier results obtained by Stinchcombe and Pimentel using transfer-matrix techniques; at higher frequencies, gaps appear in the spectrum. At low frequencies, the localization length diverges as ω-2/3. A formal connection is established between the spin glass and the one-dimensional discretized Schrödinger equation. By making use of the connection, it is shown that the theory of Derrida and Gardner, which was developed for weak potential disorder, can account quantitatively for the distribution and localization of the low-frequency magnon modes in the spin-glass model.
DEFF Research Database (Denmark)
Loft, N. J. S.; Marchukov, O. V.; Petrosyan, D.;
2016-01-01
We have developed an efficient computational method to treat long, one-dimensional systems of strongly-interacting atoms forming self-assembled spin chains. Such systems can be used to realize many spin chain model Hamiltonians tunable by the external confining potential. As a concrete demonstrat...... demonstration, we consider quantum state transfer in a Heisenberg spin chain and we show how to determine the confining potential in order to obtain nearly-perfect state transfer....
The entanglement negativity in random spin chains
Ruggiero, Paola; Calabrese, Pasquale
2016-01-01
We investigate the logarithmic negativity in strongly-disordered spin chains in the random-singlet phase. We focus on the spin-1/2 random Heisenberg chain and the random XX chain. We find that for two arbitrary intervals the disorder-averaged negativity and the mutual information are proportional to the number of singlets shared between the two intervals. Using the strong-disorder renormalization group (SDRG), we prove that the negativity of two adjacent intervals grows logarithmically with the intervals length. In particular, the scaling behavior is the same as in conformal field theory, but with a different prefactor. For two disjoint intervals the negativity is given by a universal simple function of the cross ratio, reflecting scale invariance. As a function of the distance of the two intervals, the negativity decays algebraically in contrast with the exponential behavior in clean models. We confirm our predictions using a numerical implementation of the SDRG method. Finally, we also implement DMRG simula...
Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons
Derzhko, Oleg; Richter, Johannes; Maksymenko, Mykola
2015-05-01
On a large class of lattices (such as the sawtooth chain, the kagome and the pyrochlore lattices), the quantum Heisenberg and the repulsive Hubbard models may host a completely dispersionless (flat) energy band in the single-particle spectrum. The flat-band states can be viewed as completely localized within a finite volume (trap) of the lattice and allow for construction of many-particle states, roughly speaking, by occupying the traps with particles. If the flat-band happens to be the lowest-energy one, the manifold of such many-body states will often determine the ground-state and low-temperature physics of the models at hand even in the presence of strong interactions. The localized nature of these many-body states makes possible the mapping of this subset of eigenstates onto a corresponding classical hard-core system. As a result, the ground-state and low-temperature properties of the strongly correlated flat-band systems can be analyzed in detail using concepts and tools of classical statistical mechanics (e.g., classical lattice-gas approach or percolation approach), in contrast to more challenging quantum many-body techniques usually necessary to examine strongly correlated quantum systems. In this review, we recapitulate the basic features of the flat-band spin systems and briefly summarize earlier studies in the field. The main emphasis is made on recent developments which include results for both spin and electron flat-band models. In particular, for flat-band spin systems, we highlight field-driven phase transitions for frustrated quantum Heisenberg antiferromagnets at low temperatures, chiral flat-band states, as well as the effect of a slight dispersion of a previously strictly flat-band due to nonideal lattice geometry. For electronic systems, we discuss the universal low-temperature behavior of several flat-band Hubbard models, the emergence of ground-state ferromagnetism in the square-lattice Tasaki-Hubbard model and the related Pauli
Modified algebraic Bethe ansatz for XXZ chain on the segment – II – general cases
Directory of Open Access Journals (Sweden)
S. Belliard
2015-05-01
Full Text Available The spectral problem of the Heisenberg XXZ spin-12 chain on the segment is investigated within a modified algebraic Bethe ansatz framework. We consider in this work the most general boundaries allowed by integrability. The eigenvalues and the eigenvectors are obtained. They are characterised by a set of Bethe roots with cardinality equal to N, the length of the chain, and which satisfies a set of Bethe equations with an additional term.
Enhancement of entanglement transfer in a spin chain by phase shift control
Maruyama, K; Nori, F
2006-01-01
We study the effect of a phase shift on the amount of transferrable two-spin entanglement in a spin chain. We consider a ferromagnetic Heisenberg/XY spin chain, both numerically and analytically, and two mechanisms to generate a phase shift, the Aharonov-Casher effect and the Dzyaloshinskii-Moriya interaction. In both cases, the maximum attainable entanglement is shown to be significantly enhanced, suggesting its potential usefulness in quantum information processing.
p-Laplace equation in the Heisenberg group regularity of solutions
Ricciotti, Diego
2015-01-01
This works focuses on regularity theory for solutions to the p-Laplace equation in the Heisenberg group. In particular, it presents detailed proofs of smoothness for solutions to the non-degenerate equation and of Lipschitz regularity for solutions to the degenerate one. An introductory chapter presents the basic properties of the Heisenberg group, making the coverage self-contained. The setting is the first Heisenberg group, helping to keep the notation simple and allow the reader to focus on the core of the theory and techniques in the field. Further, detailed proofs make the work accessible to students at the graduate level.
Entanglement properties in (1/2,1) mixed-spin Heisenberg systems
Sun, Z; Hu, A Z; Li, Y Q; Sun, Zhe; Wang, XiaoGuang; Hu, AnZi; Li, You-Quan
2005-01-01
By using the concept of negativity, we investigate entanglement in (1/2,1) mixed-spin Heisenberg systems. We obtain the analytical results of entanglement in small isotropic Heisenberg clusters with only nearest-neighbor (NN) interactions up to four spins and in the four-spin Heisenberg model with both NN and next-nearest-neighbor (NNN) interactions. For more spins, we numerically study effects of temperature, magnetic fields, and NNN interactions on entanglement. We study in detail the threshold value of the temperature, after which the negativity vanishes.
Some properties of H\\"older surfaces in the Heisenberg group
Donne, Enrico Le
2012-01-01
It is a folk conjecture that for alpha > 1/2 there is no alpha-Hoelder surface in the subRiemannian Heisenberg group. Namely, it is expected that there is no embedding from an open subset of R^2 into the Heisenberg group that is Hoelder continuous of order strictly greater than 1/2. The Heisenberg group here is equipped with its Carnot-Caratheodory distance. We show that, in the case that such a surface exists, it cannot be of essential bounded variation and it intersects some vertical line in at least a topological Cantor set.
Fitting magnetic field gradient with Heisenberg-scaling accuracy.
Zhang, Yong-Liang; Wang, Huan; Jing, Li; Mu, Liang-Zhu; Fan, Heng
2014-12-09
The linear function is possibly the simplest and the most used relation appearing in various areas of our world. A linear relation can be generally determined by the least square linear fitting (LSLF) method using several measured quantities depending on variables. This happens for such as detecting the gradient of a magnetic field. Here, we propose a quantum fitting scheme to estimate the magnetic field gradient with N-atom spins preparing in W state. Our scheme combines the quantum multi-parameter estimation and the least square linear fitting method to achieve the quantum Cramér-Rao bound (QCRB). We show that the estimated quantity achieves the Heisenberg-scaling accuracy. Our scheme of quantum metrology combined with data fitting provides a new method in fast high precision measurements.
Optimal uncertainty relations in a modified Heisenberg algebra
Abdelkhalek, Kais; Fiedler, Leander; Mangano, Gianpiero; Schwonnek, René
2016-01-01
Various theories that aim at unifying gravity with quantum mechanics suggest modifications of the Heisenberg algebra for position and momentum. From the perspective of quantum mechanics, such modifications lead to new uncertainty relations which are thought (but not proven) to imply the existence of a minimal observable length. Here we prove this statement in a framework of sufficient physical and structural assumptions. Moreover, we present a general method that allows to formulate optimal and state-independent variance-based uncertainty relations. In addition, instead of variances, we make use of entropies as a measure of uncertainty and provide uncertainty relations in terms of min- and Shannon entropies. We compute the corresponding entropic minimal lengths and find that the minimal length in terms of min-entropy is exactly one bit.
Scalar model of SU(N) glueball \\`a la Heisenberg
Dzhunushaliev, Vladimir
2016-01-01
Nonperturbative model of glueball is studied. The model is based on the nonperturbative quantization technique suggested by Heisenberg. 2- and 4-point Green functions for a gauge potential are expressed in terms of two scalar fields. The first scalar field describes quantum fluctuations of a subgroup $SU(n) \\subset SU(N)$, and the second one describes quantum fluctuations of coset $SU(N) / SU(n)$. An effective Lagrangian for the scalar fields is obtained. The coefficients for all terms in the Lagrangian are calculated, and it is shown that they depend on $\\dim SU(n), \\dim SU(N)$. It is demonstrated that spherically symmetric solution describing the glueball does exist.
Heisenberg-limited atom clocks based on entangled qubits.
Kessler, E M; Kómár, P; Bishof, M; Jiang, L; Sørensen, A S; Ye, J; Lukin, M D
2014-05-16
We present a quantum-enhanced atomic clock protocol based on groups of sequentially larger Greenberger-Horne-Zeilinger (GHZ) states that achieves the best clock stability allowed by quantum theory up to a logarithmic correction. Importantly the protocol is designed to work under realistic conditions where the drift of the phase of the laser interrogating the atoms is the main source of decoherence. The simultaneous interrogation of the laser phase with a cascade of GHZ states realizes an incoherent version of the phase estimation algorithm that enables Heisenberg-limited operation while extending the coherent interrogation time beyond the laser noise limit. We compare and merge the new protocol with existing state of the art interrogation schemes, and identify the precise conditions under which entanglement provides an advantage for clock stabilization: it allows a significant gain in the stability for short averaging time.
Soft Heisenberg hair on black holes in three dimensions
Afshar, Hamid; Grumiller, Daniel; Merbis, Wout; Perez, Alfredo; Tempo, David; Troncoso, Ricardo
2016-01-01
Three-dimensional Einstein gravity with negative cosmological constant admits stationary black holes that are not necessarily spherically symmetric. We propose boundary conditions for the near horizon region of these black holes that lead to a surprisingly simple near horizon symmetry algebra consisting of two affine u(1) current algebras. The symmetry algebra is essentially equivalent to the Heisenberg algebra. The associated charges give a specific example of "soft hair" on the horizon, as defined by Hawking, Perry and Strominger. We show that soft hair does not contribute to the Bekenstein-Hawking entropy of Banados-Teitelboim-Zanelli black holes and "black flower" generalizations. From the near horizon perspective the conformal generators at asymptotic infinity appear as composite operators, which we interpret in the spirit of black hole complementarity. Another remarkable feature of our boundary conditions is that they are singled out by requiring that the whole spectrum is compatible with regularity at ...
Fractionalized Fermi liquid in a Kondo-Heisenberg model
Tsvelik, A. M.
2016-10-01
The Kondo-Heisenberg model is used as a controllable tool to demonstrate the existence of a peculiar metallic state with unbroken translational symmetry where the Fermi surface volume is not controlled by the total electron density. I use a nonperturbative approach where the strongest interactions are taken into account by means of exact solution, and corrections are controllable. In agreement with the general requirements formulated by T. Senthil et al. [Phys. Rev. Lett. 90, 216403 (2003), 10.1103/PhysRevLett.90.216403], the resulting metallic state represents a fractionalized Fermi liquid where well defined quasiparticles coexist with gapped fractionalized collective excitations. The system undergoes a phase transition to an ordered phase (charge density wave or superconducting), at the transition temperature which is parametrically small in comparison to the quasiparticle Fermi energy.
Generalized Heisenberg groups and Damek-Ricci harmonic spaces
Berndt, Jürgen; Vanhecke, Lieven
1995-01-01
Generalized Heisenberg groups, or H-type groups, introduced by A. Kaplan, and Damek-Ricci harmonic spaces are particularly nice Lie groups with a vast spectrum of properties and applications. These harmonic spaces are homogeneous Hadamard manifolds containing the H-type groups as horospheres. These notes contain a thorough study of their Riemannian geometry by means of a detailed treatment of their Jacobi vector fields and Jacobi operators. Some problems are included and will hopefully stimulate further research on these spaces. The book is written for students and researchers, assuming only basic knowledge of Riemannian geometry, and it contains a brief survey of the background material needed to follow the entire treatment.
The elusive Heisenberg limit in quantum-enhanced metrology
Demkowicz-Dobrzański, Rafał; Kołodyński, Jan; Guţă, Mădălin
2012-01-01
Quantum precision enhancement is of fundamental importance for the development of advanced metrological optical experiments, such as gravitational wave detection and frequency calibration with atomic clocks. Precision in these experiments is strongly limited by the 1/√N shot noise factor with N being the number of probes (photons, atoms) employed in the experiment. Quantum theory provides tools to overcome the bound by using entangled probes. In an idealized scenario this gives rise to the Heisenberg scaling of precision 1/N. Here we show that when decoherence is taken into account, the maximal possible quantum enhancement in the asymptotic limit of infinite N amounts generically to a constant factor rather than quadratic improvement. We provide efficient and intuitive tools for deriving the bounds based on the geometry of quantum channels and semi-definite programming. We apply these tools to derive bounds for models of decoherence relevant for metrological applications including: depolarization, dephasing, spontaneous emission and photon loss. PMID:22990859
Exact Diagonalization of Heisenberg SU(N) models.
Nataf, Pierre; Mila, Frédéric
2014-09-19
Building on advanced results on permutations, we show that it is possible to construct, for each irreducible representation of SU(N), an orthonormal basis labeled by the set of standard Young tableaux in which the matrix of the Heisenberg SU(N) model (the quantum permutation of N-color objects) takes an explicit and extremely simple form. Since the relative dimension of the full Hilbert space to that of the singlet space on n sites increases very fast with N, this formulation allows us to extend exact diagonalizations of finite clusters to much larger values of N than accessible so far. Using this method, we show that, on the square lattice, there is long-range color order for SU(5), spontaneous dimerization for SU(8), and evidence in favor of a quantum liquid for SU(10).
Deformed Heisenberg algebra with minimal length and equivalence principle
Tkachuk, V M
2013-01-01
Studies in string theory and quantum gravity lead to the Generalized Uncertainty Principle (GUP) and suggest the existence of a fundamental minimal length which, as was established, can be obtained within the deformed Heisenberg algebra. The first look on the classical motion of bodies in a space with corresponding deformed Poisson brackets in a uniform gravitational field can give an impression that bodies of different mass fall in different ways and thus the equivalence principle is violated. Analyzing the kinetic energy of a composite body we find that the motion of its center of mass in the deformed space depends on some effective parameter of deformation. It gives a possibility to recover the equivalence principle in the space with deformed Poisson brackets. and thus GUP is reconciled with the equivalence principle. We also show that the independence of kinetic energy on composition leads to the recovering of the equivalence principle in the space with deformed Poisson brackets.
Local Lagrangian Formalism and Discretization of the Heisenberg Magnet Model
Karpeev, D
2004-01-01
In this paper we develop the Lagrangian and multisymplectic structures of the Heisenberg magnet (HM) model which are then used as the basis for geometric discretizations of HM. Despite a topological obstruction to the existence of a global Lagrangian density, a local variational formulation allows one to derive local conservation laws using a version of N\\"other's theorem from the formal variational calculus of Gelfand-Dikii. Using the local Lagrangian form we extend the method of Marsden, Patrick and Schkoller to derive local multisymplectic discretizations directly from the variational principle. We employ a version of the finite element method to discretize the space of sections of the trivial magnetic spin bundle $N = M\\times S^2$ over an appropriate space-time $M$. Since sections do not form a vector space, the usual FEM bases can be used only locally with coordinate transformations intervening on element boundaries, and conservation properties are guaranteed only within an element. We discuss possible w...
Pauli-Heisenberg Oscillations in Electron Quantum Transport.
Thibault, Karl; Gabelli, Julien; Lupien, Christian; Reulet, Bertrand
2015-06-12
We measure the current fluctuations emitted by a normal-metal-insulator-normal-metal tunnel junction with a very wide bandwidth, from 0.3 to 13 GHz, down to very low temperature T=35 mK. This allows us to perform the spectroscopy (i.e., measure the frequency dependence) of thermal noise (no dc bias, variable temperature) and shot noise (low temperature, variable dc voltage bias). Because of the very wide bandwidth of our measurement, we deduce the current-current correlator in the time domain. We observe the thermal decay of this correlator as well as its oscillations with a period h/eV, a direct consequence of the effect of the Pauli and Heisenberg principles in quantum electron transport.
Classical Heisenberg spins on a hexagonal lattice with Kitaev couplings.
Chandra, Samarth; Ramola, Kabir; Dhar, Deepak
2010-09-01
We analyze the low temperature properties of a system of classical Heisenberg spins on a hexagonal lattice with Kitaev couplings. For a lattice of 2N sites with periodic boundary conditions, the ground states form an (N+1) dimensional manifold. We show that the ensemble of ground states is equivalent to that of a solid-on-solid model with continuously variable heights and nearest neighbor interactions, at a finite temperature. For temperature T tending to zero, all ground states have equal weight, and there is no order by disorder in this model. We argue that the bond-energy bond-energy correlations at distance R decay as 1/R2 at zero temperature. This is verified by Monte Carlo simulations. We also discuss the relation to the quantum spin- S Kitaev model for large S, and obtain lower and upper bounds on the ground-state energy of the quantum model.
Optimal uncertainty relations in a modified Heisenberg algebra
Abdelkhalek, Kais; Chemissany, Wissam; Fiedler, Leander; Mangano, Gianpiero; Schwonnek, René
2016-12-01
Various theories that aim at unifying gravity with quantum mechanics suggest modifications of the Heisenberg algebra for position and momentum. From the perspective of quantum mechanics, such modifications lead to new uncertainty relations that are thought (but not proven) to imply the existence of a minimal observable length. Here we prove this statement in a framework of sufficient physical and structural assumptions. Moreover, we present a general method that allows us to formulate optimal and state-independent variance-based uncertainty relations. In addition, instead of variances, we make use of entropies as a measure of uncertainty and provide uncertainty relations in terms of min and Shannon entropies. We compute the corresponding entropic minimal lengths and find that the minimal length in terms of min entropy is exactly 1 bit.
Spin-wave multiple excitations in nanoscale classical Heisenberg antiferromagnets
Energy Technology Data Exchange (ETDEWEB)
Hou, Zhuofei [University of Georgia, Athens; Landau, David P [University of Georgia, Athens; Stocks, George Malcolm [ORNL; Brown, G. [Florida State University, Tallahassee
2015-02-17
Monte Carlo and spin dynamics techniques have been used to perform large-scale simulations of the dynamic behavior of a nanoscale, classical, Heisenberg antiferromagnet on a simple-cubic lattice with linear sizes L≤ 40 at a temperature below the Neel temperature. In this study, nanoparticles are modeled with completely free boundary conditions, i.e., six free surfaces, and nanofilms are modeled with two free surfaces in the spatial z direction and periodic boundaries parallel to the surfaces in the xy direction, which are compared to the infinite system with periodic boundary conditions. The temporal evolutions of spin configurations were determined numerically from coupled equations of motion for individual spins using a fast spin dynamics algorithm with the fourth-order Suzuki-Trotter decomposition of exponential operators, with initial spin configurations generated by Monte Carlo simulations. The local dynamic structure factor S(q,ω) was calculated from the local space- and time-displaced spin-spin correlation function. Multiple excitation peaks for wave vectors within the first Brillouin zone appear in the spin-wave spectra of the transverse component of dynamic structure factor S^{T} (q,ω) in the nanoscale classical Heisenberg antiferromagnet, which are lacking if periodic boundary conditions are used. With the assumption of q-space spin-wave reflections with broken momentum conservation due to free-surface confinements, we successfully explained those spectra quantitatively in the linear dispersion region. Meanwhile, we also observed two unexpected quantized spin-wave excitation modes in the spatial z direction in nanofilms for S^{T} (q,ω) not expected in bulk systems. In conclusion, the results of this study indicate the presence of unexpected forms of spin-wave excitation behavior that have yet to be observed experimentally but could be directly tested through neutron scattering experiments on nanoscale RbMnF_{3} particles or
Quantum chaos in the Heisenberg spin chain: The effect of Dzyaloshinskii-Moriya interaction
Vahedi, J.; Ashouri, A.; Mahdavifar, S.
2016-10-01
Using one-dimensional spin-1/2 systems as prototypes of quantum many-body systems, we study the emergence of quantum chaos. The main purpose of this work is to answer the following question: how the spin-orbit interaction, as a pure quantum interaction, may lead to the onset of quantum chaos? We consider the three integrable spin-1/2 systems: the Ising, the XX, and the XXZ limits and analyze whether quantum chaos develops or not after the addition of the Dzyaloshinskii-Moriya interaction. We find that depending on the strength of the anisotropy parameter, the answer is positive for the XXZ and Ising models, whereas no such evidence is observed for the XX model. We also discuss the relationship between quantum chaos and thermalization.
Hardy-Type Inequalities on H-Type Groups and Anisotropic Heisenberg Groups
Institute of Scientific and Technical Information of China (English)
Yongyang JIN
2008-01-01
The author obtains some weighted Hardy-type inequalities on H-type groups and anisotropic Heisenberg groups.These inequalities generalize some recent results due to N.Garofalo,E.Lanconelli,I.Kombe and P.Niu et al.
Heisenberg Algebra in the Bargmann-Fock Space with Natural Cutoffs
Directory of Open Access Journals (Sweden)
Maryam Roushan
2014-01-01
Full Text Available We construct a Heisenberg algebra in Bargmann-Fock space in the presence of natural cutoffs encoded as minimal length, minimal momentum, and maximal momentum through a generalized uncertainty principle.
Uncertainty Einstein, Heisenberg, Bohr, and the struggle for the soul of science
Lindley, David
2007-01-01
The uncertainty in this delightful book refers to Heisenberg's Uncertainty Principle, an idea first postulated in 1927 by physicist Werner Heisenberg in his attempt to make sense out of the developing field of quantum mechanics. As Lindley so well explains it, the concept of uncertainty shook the philosophical underpinnings of science. It was Heisenberg's work that, to a great extent, kept Einstein from accepting quantum mechanics as a full explanation for physical reality. Similarly, it was the Uncertainty Principle that demonstrated the limits of scientific investigation: if Heisenberg is correct there are some aspects of the physical universe that are to remain beyond the reach of scientists. As he has done expertly in books like Boltzmann's Atom, Lindley brings to life a critical period in the history of science, explaining complex issues to the general reader, presenting the major players in an engaging fashion, delving into the process of scientific discovery and discussing the interaction between scien...
Blow-up of solutions to parabolic inequalities in the Heisenberg group
Directory of Open Access Journals (Sweden)
Ibtehal Azman
2015-06-01
Full Text Available We establish a Fujita-type theorem for the blow-up of nonnegative solutions to a certain class of parabolic inequalities in the Heisenberg group. Our proof is based on a duality argument.
Waste Not, Want Not: Heisenberg-Limited Metrology With Information Recycling
Haine, Simon A; Lang, Matthias D; Caves, Carlton M
2014-01-01
Information recycling has been shown to improve the sensitivity of interferometers when the input quantum state has been partially transferred from some donor system. In this paper we demonstrate that when the quantum state of this donor system is from a particular class of Heisenberg-limited states, information recycling yields a Heisenberg-limited phase measurement. Crucially, this result holds irrespective of the fraction of the quantum state transferred to the interferometer input and also for a general class of number-conserving quantum-state-transfer processes, including ones that destroy the first-order phase coherence between the branches of the interferometer. This result could have significant applications in Heisenberg-limited atom interferometry, where the quantum state is transferred from a Heisenberg-limited photon source, and in optical interferometry where the loss can be monitored.
Neel order in the two-dimensional S=1/2 Heisenberg Model
Löw, Ute
2007-01-01
The existence of Neel order in the S=1/2 Heisenberg model on the square lattice at T=0 is shown using inequalities set up by Kennedy, Lieb and Shastry in combination with high precision Quantum Monte Carlo data.
Employing Taylor and Heisenberg subfilter viscosities to simulate turbulent statistics in LES models
Degrazia, G. A.; Rizza, U.; Puhales, F. S.; Welter, G. S.; Acevedo, O. C.; Maldaner, S.
2012-02-01
A turbulent subfilter viscosity for Large Eddy Simulation (LES) based on the Taylor statistical diffusion theory is proposed. This viscosity is described in terms of a velocity variance and a time scale, both associated to the inertial subrange. This new subfilter viscosity contains a cutoff wavenumber kc, presenting an identical form (differing by a constant) to the Heisenberg subfilter viscosity. Therefore, both subfilter viscosities are described in terms of a sharp division between large and small wavenumbers of a turbulent flow and, henceforth, Taylor and Heisenberg subfilter viscosities are in agreement with the sharp Fourier filtering operation, frequently employed in LES models. Turbulent statistics of different orders, generated from atmospheric boundary layer simulations employing both Taylor and Heisenberg subfilter viscosities have been compared with observations and results provided by other simulations. The comparison shows that the LES model utilizing the approaches of Taylor and Heisenberg reproduces these turbulent statistics correctly in different vertical regions of a planetary convective boundary layer (CBL).
THE UNIFORMLY BOUNDEDNESS OF THE RIESZ TRANSFORMS ON THE CAYLEY HEISENBERG GROUPS
Institute of Scientific and Technical Information of China (English)
Luan Jingwen; Zhu Fuliu
2008-01-01
In this article, the authors estimate some functions by using the explicit ex-pression of the heat kernels for the Cayley Heisenberg groups, and then prove the uniform boundedneas of the Riesz transforms on these nilpotent Lie groups.
SOME LIOUVILLE TYPE THEOREMS FOR THE P-SUB-LAPLACIAN ON THE GROUP OF HEISENBERG TYPE
Institute of Scientific and Technical Information of China (English)
Yuan Zixia; Niu Pengcheng
2008-01-01
In this paper we prove some Liouville type results for the p-sub-Laplacian on the group of Heisenberg type. A strong maximum principle and a Hopf type principle concerning p-sub-Laplacian are established.
High-field spin dynamics of antiferromagnetic quantum spin chains
DEFF Research Database (Denmark)
Enderle, M.; Regnault, L.P.; Broholm, C.;
2000-01-01
The characteristic internal order of macroscopic quantum ground states in one-dimensional spin systems is usually not directly accessible, but reflected in the spin dynamics and the field dependence of the magnetic excitations. In high magnetic fields quantum phase transitions are expected. We...... present recent work on the high-field spin dynamics of the S = I antiferromagnetic Heisenberg chains NENP (Haldane ground state) and CsNiCl3 (quasi-1D HAF close to the quantum critical point), the uniform S = 1/2 chain CTS, and the spin-Peierls system CuGeO3. (C) 2000 Elsevier Science B,V. All rights...
A Hardy Inequality with Remainder Terms in the Heisenberg Group and the Weighted Eigenvalue Problem
Directory of Open Access Journals (Sweden)
Dou Jingbo
2007-01-01
Full Text Available Based on properties of vector fields, we prove Hardy inequalities with remainder terms in the Heisenberg group and a compact embedding in weighted Sobolev spaces. The best constants in Hardy inequalities are determined. Then we discuss the existence of solutions for the nonlinear eigenvalue problems in the Heisenberg group with weights for the -sub-Laplacian. The asymptotic behaviour, simplicity, and isolation of the first eigenvalue are also considered.
A Hardy Inequality with Remainder Terms in the Heisenberg Group and the Weighted Eigenvalue Problem
Directory of Open Access Journals (Sweden)
Zixia Yuan
2007-12-01
Full Text Available Based on properties of vector fields, we prove Hardy inequalities with remainder terms in the Heisenberg group and a compact embedding in weighted Sobolev spaces. The best constants in Hardy inequalities are determined. Then we discuss the existence of solutions for the nonlinear eigenvalue problems in the Heisenberg group with weights for the p-sub-Laplacian. The asymptotic behaviour, simplicity, and isolation of the first eigenvalue are also considered.
On First Order Interpolation Inequalities with Weights on the Heisenberg Group
Institute of Scientific and Technical Information of China (English)
Ya Zhou HAN; Peng Cheng NIU; Shu Tao ZHANG
2011-01-01
In this paper,sufficient and necessary conditions for the first order interpolation inequalities with weights on the Heisenberg group are given.The necessity is discussed by polar coordinates changes of the Heisenberg group.Establishing a class of Hardy type inequalities via a new representation formula for functions and Hardy-Sobolev type inequalities by interpolation,we derive the sufficiency.Finally,sharp constants for Hardy type inequalities are determined.
Nicolescu, B
2004-01-01
The ln**2 behaviour of total cross sections, first obtained by Heisenberg 50 years ago, receives now increased interest both on phenomenological and theoretical levels. We present a modification of the Heisenberg's model in connection with the presence of glueballs and we show that it leads to a realistic description of all existing hadron total cross-section data, in agreement with the COMPETE analysis.
Kawamura, Hikaru; Arimori, Takuya
2002-02-18
Ordering of the geometrically frustrated two-dimensional Heisenberg antiferromagnet on a pyrochlore slab is studied by Monte Carlo simulations. In contrast to the kagomé Heisenberg antiferromagnet, the model exhibits locally noncoplanar spin structures at low temperatures, bearing nontrivial chiral degrees of freedom. Under certain conditions, the model exhibits a novel Kosterlitz-Thouless-type transition at a finite temperature associated with these chiral degrees of freedom.
Evidence for a bicritical point in the XXZ Heisenberg antiferromagnet on a simple cubic lattice.
Selke, Walter
2011-04-01
The classical Heisenberg antiferromagnet with uniaxial exchange anisotropy (XXZ model) in a field on a simple cubic lattice is studied with the help of extensive Monte Carlo simulations. We analyze, in particular, various staggered susceptibilities and Binder cumulants and present clear evidence for the triple point of the antiferromagnetic, spin-flop, and paramagnetic phases being a bicritical point with Heisenberg symmetry. Results are compared to previous predictions applying various theoretical approaches.
Thermal quantum discord in Heisenberg models with Dzyaloshinski-Moriya interaction
Institute of Scientific and Technical Information of China (English)
Wang Lin-Cheng; Yan Jun-Yan; Yi Xue-Xi
2011-01-01
We study the quantum discord of the bipartite Heisenberg model with the Dzyaloshinski-Moriya(DM)interaction in thermal equilibrium state and discuss the effect of the DM interaction on the quantum discord.The quantum entanglement of the system is also discussed and compared with quantum discord. Our results show that the quantum discord may reveal more properties of the system than quantum entanglement and the DM interaction may play an important role in the Heisenberg model.
Blockspin Cluster Algorithms for Quantum Spin Systems
Wiese, U J
1992-01-01
Cluster algorithms are developed for simulating quantum spin systems like the one- and two-dimensional Heisenberg ferro- and anti-ferromagnets. The corresponding two- and three-dimensional classical spin models with four-spin couplings are maped to blockspin models with two-blockspin interactions. Clusters of blockspins are updated collectively. The efficiency of the method is investigated in detail for one-dimensional spin chains. Then in most cases the new algorithms solve the problems of slowing down from which standard algorithms are suffering.
Branco, N S; de Sousa, J Ricardo; Ghosh, Angsula
2008-03-01
Using a real-space renormalization-group approximation, we study the anisotropic quantum Heisenberg model on hierarchical lattices, with interactions following aperiodic sequences. Three different sequences are considered, with relevant and irrelevant fluctuations, according to the Luck-Harris criterion. The phase diagram is discussed as a function of the anisotropy parameter Delta (such that Delta=0 and 1 correspond to the isotropic Heisenberg and Ising models, respectively). We find three different types of phase diagrams, with general characteristics: the isotropic Heisenberg plane is always an invariant one (as expected by symmetry arguments) and the critical behavior of the anisotropic Heisenberg model is governed by fixed points on the Ising-model plane. Our results for the isotropic Heisenberg model show that the relevance or irrelevance of aperiodic models, when compared to their uniform counterpart, is as predicted by the Harris-Luck criterion. A low-temperature renormalization-group procedure was applied to the classical isotropic Heisenberg model in two-dimensional hierarchical lattices: the relevance criterion is obtained, again in accordance with the Harris-Luck criterion.
Heisenberg XX自旋环中的纠缠开关%Entanglement Switch in Heisenberg XX Spin Rings
Institute of Scientific and Technical Information of China (English)
杨海超; 揭泉林
2012-01-01
This paper is devoted to analyse the three-qubit Heisenberg XX rings in a uniform magnetic field, and by controlling of the coupling of a site we can change the entanglement between other two sites. We find that thermal entanglement exhibits a platform-like behaviour and entangled value is equal to 1 when coupling of the site which was controlled is small than that was not controlled,the width of the platform-like region could he controlled by changing the coupling between was not sites, This novel property may be used as a quantum entanglement switch. At the same time, we analyse the situation that two sites were controlled, the entanglement maximal switch still can be realized. Moreover, we find that there are linear relation in the spin-spin interactions.%研究了在均匀磁场中的三格点Heisenberg XX自旋环,通过控制一个格点的耦合参数,来调控另外两个格点之间的纠缠.理论上发现当控制格点的耦合参数比未控制格点的耦合参数小时,未控制格点间的纠缠随磁场变化会出现一个纠缠值为1的平台.在较低温度下,平台的宽度与未控制格点间的耦合参数值相等,是一个很好的纠缠开关.同时,分析了存在两个控制格点的情况,也可以得到纠缠值为1的开关,并发现自旋相互作用具有线性关系.
Generando entrelazamiento en cadenas XY - (Generating entanglement in XY chains)
Schmiegelow, C T
2006-01-01
Se estudia en este trabajo la capacidad de generar entrelazamiento de una cadena de espines con acoplamiento de Heisenberg XY y un campo magnetico uniforme a partir de un estado inicial en el que los espines estan completamente alineados. Se encuentra que la capacidad de generar estados entrelazados no muestra un comportamiento monotono con el campo presentando, en cambio, plateaus y resonancias. Tambien se muestra que, a pesar de que la anisotropia es necesaria para que se generen estados entrelazados, una mayor anisotropia no implica necesariamente mejores condiciones para generar entrelazamiento que sirva para usarse en una computadora cuantica. Inclusive, se observa que, se genera una cantidad finita de entrelazamiento en el limite de pequena anisotropia. (The maximum entanglement reached by an initially fully aligned state evolving in a XY Heisenberg spin chain placed in a uniform transverse magnetic field is studied. It is shown that the capacity to create entangled states (both of one qubit with the re...
Wong, Chun Wa; Yasui, Kosuke
2006-06-01
The one-dimensional fall of a folded chain with one end suspended from a rigid support and a chain falling from a resting heap on a table is studied. Because their Lagrangians contain no explicit time dependence, the falling chains are conservative systems. Their equations of motion are shown to contain a term that enforces energy conservation when masses are transferred between subchains. We show that Cayley's 1857 energy nonconserving solution for a chain falling from a resting heap is incorrect because it neglects the energy gained when a link leaves a subchain. The maximum chain tension measured by Calkin and March for the falling folded chain is given a simple if rough interpretation. Other aspects of the falling folded chain are briefly discussed.
Frustrated square lattice Heisenberg model and magnetism in Iron Telluride
Zaliznyak, Igor; Xu, Zhijun; Gu, Genda; Tranquada, John; Stone, Matthew
2011-03-01
We have measured spin excitations in iron telluride Fe1.1Te, the parent material of (1,1) family of iron-based superconductors. It has been recognized that J1-J2-J3 frustrated Heisenberg model on a square lattice might be relevant for the unusual magnetism and, perhaps, the superconductivity in cuprates [1,2]. Recent neutron scattering measurements show that similar frustrated model might also provide reasonable account for magnetic excitations in iron pnictide materials. We find that it also describes general features of spin excitations in FeTe parent compound observed in our recent neutron measurements, as well as in those by other groups. Results imply proximity of magnetic system to the limit of extreme frustration. Selection of spin ground state under such conditions could be driven by weak extrinsic interactions, such as lattice distortion, or strain. Consequently, different nonuniversal types of magnetic order could arise, both commensurate and incommensurate. These are not necessarily intrinsic to an ideal J1-J2-J3 model, but might result from lifting of its near degeneracy by weak extrinsic perturbations.
Electromagnetic soliton propagation in an anisotropic Heisenberg helimagnet
Energy Technology Data Exchange (ETDEWEB)
Saravanan, M., E-mail: saravanan_manickam@yahoo.com
2014-08-22
We study the nonlinear spin dynamics of Heisenberg helimagnet under the effect of electromagnetic wave (EM) propagation. The basic dynamical equation of the spin evolution governed by Landau–Lifshitz equation resembles the director dynamics of the twist in a cholestric liquid crystal. With the use of reductive perturbation technique the perturbation is invoked for the spin magnetization and magnetic field components of the propagating electromagnetic wave. A steady-state solution is derived for the weakly nonlinear regime and for the next order, the components turn around s plane perpendicular to the propagation direction. It is found that as the electromagnetic wave propagates in the medium, both the magnetization and magnetic field modulate in the form of kink soliton modes by introducing amplitude fluctuation in the tail part of the same. - Highlights: • The propagation of electromagnetic wave in helimagnet is investigated. • The magnetization and electromagnetic wave modulates in the form of solitons. • The exact solutions of the spin systems is derived using homogeneous balance method.
Bipartite entanglement in spin-1/2Heisenberg model
Institute of Scientific and Technical Information of China (English)
HU Ming-Liang; TIAN Dong-Ping
2008-01-01
The bipartite entanglement of the two-and three-spin Heisenberg model was investigated by using the concept of negativity.It is found that for the ground-state entanglement of the two-spin model,the negativity always decreases as B increases if A Δ＜y-1,and it may keep a steady value of 0.5in the region of B＜J[(Δ+1)2-y2]1/2if Δ＞y-1,while for that of the three-spin model,the negativity exhibits square wave structures if y=0 or Δ=0.For thermal states,there are two areas showing entanglement,namely,the main region and the sub-region.The main region exists only when Δ＞Δc(Δc1=and(y2-1)/2for the 2-and 3-spin model respectively)and extends in terms of B and T as Δ increases,while the sub-region survives only when y≠0 and shrinks in terms of B and T as Δ increases.
Reducing Uncertainty: Implementation of Heisenberg Principle to Measure Company Performance
Directory of Open Access Journals (Sweden)
Anna Svirina
2015-08-01
Full Text Available The paper addresses the problem of uncertainty reduction in estimation of future company performance, which is a result of wide range of enterprise's intangible assets probable efficiency. To reduce this problem, the paper suggests to use quantum economy principles, i.e. implementation of Heisenberg principle to measure efficiency and potential of intangible assets of the company. It is proposed that for intangibles it is not possible to estimate both potential and efficiency at a certain time point. To provide a proof for these thesis, the data on resources potential and efficiency from mid-Russian companies was evaluated within deterministic approach, which did not allow to evaluate probability of achieving certain resource efficiency, and quantum approach, which allowed to estimate the central point around which the probable efficiency of resources in concentrated. Visualization of these approaches was performed by means of LabView software. It was proven that for tangible assets performance estimation a deterministic approach should be used; while for intangible assets the quantum approach allows better quality of future performance prediction. On the basis of these findings we proposed the holistic approach towards estimation of company resource efficiency in order to reduce uncertainty in modeling company performance.
Mott glass phase in a diluted bilayer Heisenberg quantum antiferromagnet
Ma, Nv-Sen; Sandvik, Anders W.; Yao, Dao-Xin
2015-09-01
We use quantum Monte Carlo simulations to study a dimer-diluted S = 1/2 Heisenberg model on a bilayer square lattice with intralayer interaction J1 and interlayer interaction J2. Below the classical percolation threshold pc, the system has three phases reachable by tuning the interaction ratio g = J2/J1: a Néel ordered phase, a gapless quantum glass phase, and a gapped quantum paramagnetic phase. We present the ground-state phase diagram in the plane of dilution p and interaction ratio g. The quantum glass phase is certified to be of the gapless Mott glass type, having a uniform susceptibility vanishing at zero temperature T and following a stretched exponential form at T > 0; χu exp(-b/Tα) with α < 1. At the phase transition point from Neel ordered to Mott glass, we find that the critical exponents are different from those of the clean system described by the standard O(3) universality class in 2+1 dimensions.
Spectrum of a duality-twisted Ising quantum chain
Grimm, U
2002-01-01
The Ising quantum chain with a peculiar twisted boundary condition is considered. This boundary condition, first introduced in the framework of the spin-1/2 XXZ Heisenberg quantum chain, is related to the duality transformation, which becomes a symmetry of the model at the critical point. Thus, at the critical point, the Ising quantum chain with the duality-twisted boundary is translationally invariant, similar as in the case of the usual periodic or antiperiodic boundary conditions. The complete energy spectrum of the Ising quantum chain is calculated analytically for finite systems, and the conformal properties of the scaling limit are investigated. This provides an explicit example of a conformal twisted boundary condition and a corresponding generalised twisted partition function.
Aperiodic quantum XXZ chains: Renormalization-group results
Vieira, André P.
2005-04-01
We report a comprehensive investigation of the low-energy properties of antiferromagnetic quantum XXZ spin chains with aperiodic couplings. We use an adaptation of the Ma-Dasgupta-Hu renormalization-group method to obtain analytical and numerical results for the low-temperature thermodynamics and the ground-state correlations of chains with couplings following several two-letter aperiodic sequences, including the quasiperiodic Fibonacci and other precious-mean sequences, as well as sequences inducing strong geometrical fluctuations. For a given aperiodic sequence, we argue that in the easy-plane anisotropy regime, intermediate between the XX and Heisenberg limits, the general scaling form of the thermodynamic properties is essentially given by the exactly known XX behavior, providing a classification of the effects of aperiodicity on XXZ chains. We also discuss the nature of the ground-state structures and their comparison with the random-singlet phase characteristic of random-bond chains.
The expanded triangular Kitaev–Heisenberg model in the full parameter space
Energy Technology Data Exchange (ETDEWEB)
Yao, Xiaoyan, E-mail: yaoxiaoyan@gmail.com
2014-06-13
The classical Kitaev–Heisenberg model on the triangular lattice is investigated by simulation in its full parameter space together with the next-nearest neighboring Heisenberg interaction or the single-ion anisotropy. The variation of the system is demonstrated directly by the joint density of states (DOS) depending on energy and magnetization obtained from Wang–Landau algorithm. The Metropolis Monte Carlo simulation and the zero-temperature Glauber dynamics are performed to show the internal energy, the correlation functions and spin configurations at zero temperature. It is revealed that two types of DOS (U and inverse U) divide the whole parameter range into two main parts with antiferromagnetic and ferromagnetic features respectively. In the parameter range of U type DOS, the mixed frustration from the triangular geometry and the Kitaev interaction produces rich phases, which are influenced in different ways by the next-nearest neighboring Heisenberg interaction and the single-ion anisotropy. - Highlights: • The expanded triangular Kitaev–Heisenberg model is investigated by simulation. • The density of states is shown in the full parameter space. • Rich low-temperature phases are induced by the mixed frustration. • The next nearest-neighboring Heisenberg interaction influences the phases. • The single-ion anisotropy modifies the shape of the density of states.
Ground state of a spin-1/2 Heisenberg-Ising two-leg ladder with XYZ intra-rung coupling
Directory of Open Access Journals (Sweden)
T. Verkholyak
2013-03-01
Full Text Available The quantum spin-1/2 two-leg ladder with an anisotropic XYZ Heisenberg intra-rung interaction and Ising inter-rung interactions is treated by means of a rigorous approach based on the unitary transformation. The particular case of the considered model with X-X intra-rung interaction resembles a quantum compass ladder with additional frustrating diagonal Ising interactions. Using an appropriately chosen unitary transformation, the model under investigation may be reduced to a transverse Ising chain with composite spins, and one may subsequently find the ground state quite rigorously. We obtain a ground-state phase diagram and analyze the interplay of the competition between several factors: the XYZ anisotropy in the Heisenberg intra-rung coupling, the Ising interaction along the legs, and the frustrating diagonal Ising interaction. The investigated model shows extraordinarily diverse ground-state phase diagrams including several unusual quantum ordered phases, two different disordered quantum paramagnetic phases, as well as discontinuous or continuous quantum phase transitions between those phases.
Cambou, A D; Hamm, E; Hanna, J A; Menon, N; Santangelo, C D; Walsh, L
2012-01-01
A loop of chain can move along its own tangents, maintaining a steady shape. An open-ended chain undergoing a nontrivial motion must change its shape. One consequence is that chains pulled around objects will fail to follow the contours of the objects, unwrapping themselves instead. This short note accompanies a fluid dynamics video submission (83068) to the APS DFD Gallery of Fluid Motion 2012.
Wong, C W; Wong, Chun Wa; Yasui, Kosuke
2006-01-01
The one-dimensional falling motion of a bungee chain suspended from a rigid support and of a chain falling from a resting heap on a table is studied. Their Lagrangians are found to contain no explicit time dependence. As a result, these falling chains are conservative systems. Each of their Lagrange's equations of motion is shown to contain a term that enforces energy conservation when masses are transferred between subchains. We show in particular that Cayley's 1857 energy nonconserving solution for a chain falling from a resting heap is incorrect because it neglects the energy gained when the transferred link is emitted by the emitting subchain. The maximum chain tension measured by Calkin and March for the falling bungee chain is given a simple if rough interpretation. In the simplified one-dimensional treatment, the kinetic energy of the center of mass of the falling bungee chain is found to be converted by the chain tension at the rigid support into the internal kinetic energy of the chain. However, as t...
Thomsen, Dietrick E.
1976-01-01
Presented is an insight into man's idea about physics and being a physicist in the days when Heisenberg, P. A. M. Dirac, Louis de Broglic and other famous physicists were young men. Heisenberg is compared to Newton, inventing new math as he needed it. Emphasis is placed on the fact that he was not a Nazi sympathizer. (EB)
Experimental violation and reformulation of the Heisenberg's error-disturbance uncertainty relation
Baek, So-Young; Kaneda, Fumihiro; Ozawa, Masanao; Edamatsu, Keiichi
2013-07-01
The uncertainty principle formulated by Heisenberg in 1927 describes a trade-off between the error of a measurement of one observable and the disturbance caused on another complementary observable such that their product should be no less than the limit set by Planck's constant. However, Ozawa in 1988 showed a model of position measurement that breaks Heisenberg's relation and in 2003 revealed an alternative relation for error and disturbance to be proven universally valid. Here, we report an experimental test of Ozawa's relation for a single-photon polarization qubit, exploiting a more general class of quantum measurements than the class of projective measurements. The test is carried out by linear optical devices and realizes an indirect measurement model that breaks Heisenberg's relation throughout the range of our experimental parameter and yet validates Ozawa's relation.
Spin-Ice State of the Quantum Heisenberg Antiferromagnet on the Pyrochlore Lattice.
Huang, Yuan; Chen, Kun; Deng, Youjin; Prokof'ev, Nikolay; Svistunov, Boris
2016-04-29
We study the low-temperature physics of the SU(2)-symmetric spin-1/2 Heisenberg antiferromagnet on a pyrochlore lattice and find "fingerprint" evidence for the thermal spin-ice state in this frustrated quantum magnet. Our conclusions are based on the results of bold diagrammatic Monte Carlo simulations, with good convergence of the skeleton series down to the temperature T/J=1/6. The identification of the spin-ice state is done through a remarkably accurate microscopic correspondence for the static structure factor between the quantum Heisenberg, classical Heisenberg, and Ising models at all accessible temperatures, and the characteristic bowtie pattern with pinch points observed at T/J=1/6. The dynamic structure factor at real frequencies (obtained by the analytic continuation of numerical data) is consistent with diffusive spinon dynamics at the pinch points.
Near-Heisenberg-limited atomic clocks in the presence of decoherence.
Borregaard, J; Sørensen, A S
2013-08-30
The ultimate stability of atomic clocks is limited by the quantum noise of the atoms. To reduce this noise it has been suggested to use entangled atomic ensembles with reduced atomic noise. Potentially this can push the stability all the way to the limit allowed by the Heisenberg uncertainty relation, which is denoted the Heisenberg limit. In practice, however, entangled states are often more prone to decoherence, which may prevent reaching this performance. Here we present an adaptive measurement protocol that in the presence of a realistic source of decoherence enables us to get near-Heisenberg-limited stability of atomic clocks using entangled atoms. The protocol may thus realize the full potential of entanglement for quantum metrology despite the detrimental influence of decoherence.
Magnetization Process and Magnetocaloric Effect of the Spin-1/2 XXZ Heisenberg Cuboctahedron
Karľová, Katarína; Strečka, Jozef
2016-10-01
Magnetic properties of the spin-1/2 XXZ Heisenberg cuboctahedron are examined using exact numerical diagonalization depending on a relative strength of the exchange anisotropy. While the Ising cuboctahedron exhibits in a low-temperature magnetization curve only one-third magnetization plateau, the XXZ Heisenberg cuboctahedron displays another four intermediate plateaux at zero, one-sixth, one-half and two-thirds of the saturation magnetization. The novel magnetization plateaux generally extend over a wider range of magnetic fields with increasing of a quantum (xy) part of the XXZ exchange interaction. It is shown that the XXZ Heisenberg cuboctahedron exhibits in the vicinity of all magnetization jumps anomalous thermodynamic behavior accompanied by an enhanced magnetocaloric effect.
Spin-Ice State of the Quantum Heisenberg Antiferromagnet on the Pyrochlore Lattice
Huang, Yuan; Chen, Kun; Deng, Youjin; Prokof'ev, Nikolay; Svistunov, Boris
2016-04-01
We study the low-temperature physics of the SU(2)-symmetric spin-1 /2 Heisenberg antiferromagnet on a pyrochlore lattice and find "fingerprint" evidence for the thermal spin-ice state in this frustrated quantum magnet. Our conclusions are based on the results of bold diagrammatic Monte Carlo simulations, with good convergence of the skeleton series down to the temperature T /J =1 /6 . The identification of the spin-ice state is done through a remarkably accurate microscopic correspondence for the static structure factor between the quantum Heisenberg, classical Heisenberg, and Ising models at all accessible temperatures, and the characteristic bowtie pattern with pinch points observed at T /J =1 /6 . The dynamic structure factor at real frequencies (obtained by the analytic continuation of numerical data) is consistent with diffusive spinon dynamics at the pinch points.
Low-temperature Spin-Ice State of Quantum Heisenberg Magnets on Pyrochlore Lattice
Huang, Yuan; Chen, Kun; Deng, Youjin; Prokof'ev, Nikolay; Svistunov, Boris
We establish that the isotropic spin-1/2 Heisenberg antiferromagnet on pyrochlore lattice enters a spin-ice state at low, but finite, temperature. Our conclusions are based on results of the bold diagrammatic Monte Carlo simulations that demonstrate good convergence of the skeleton series down to temperature T = J/6. The ``smoking gun'' identification of the spin-ice state is done through a remarkably accurate microscopic correspondence for static spin-spin correlation function between the quantum Heisenberg and classical Heisenberg/Ising models at all accessible temperatures. In particular, at T/J = 1/6, the momentum dependence shows a characteristic bow-tie pattern with pinch points. By numerical analytical continuation method, we also obtain the dynamic structure factor at real frequencies, showing a diffusive spinon dynamics at pinch points and spin wave continuum along the nodal lines.?
Experimental violation and reformulation of the Heisenberg's error-disturbance uncertainty relation.
Baek, So-Young; Kaneda, Fumihiro; Ozawa, Masanao; Edamatsu, Keiichi
2013-01-01
The uncertainty principle formulated by Heisenberg in 1927 describes a trade-off between the error of a measurement of one observable and the disturbance caused on another complementary observable such that their product should be no less than the limit set by Planck's constant. However, Ozawa in 1988 showed a model of position measurement that breaks Heisenberg's relation and in 2003 revealed an alternative relation for error and disturbance to be proven universally valid. Here, we report an experimental test of Ozawa's relation for a single-photon polarization qubit, exploiting a more general class of quantum measurements than the class of projective measurements. The test is carried out by linear optical devices and realizes an indirect measurement model that breaks Heisenberg's relation throughout the range of our experimental parameter and yet validates Ozawa's relation.
K-theory, cyclic cohomology and pairings for quantum Heisenberg manifolds
DEFF Research Database (Denmark)
Gabriel, Olivier
2013-01-01
The C*-algebras called quantum Heisenberg manifolds (QHMs) were introduced by Rieffel in 1989 as strict deformation quantizations of Heisenberg manifolds. It was later shown that they are also examples of generalized crossed products. In this article, we compute the pairings of K-theory and cyclic...... cohomology on the QHM. Combining these calculations with other results proved elsewhere, we also determine the periodic cyclic homology and cohomology of these algebras, and obtain explicit bases of the periodic cyclic cohomology of the QHM. We further isolate bases of periodic cyclic homology, expressed...
Un-equivalency Theorem of Deformed Heisenberg-Weyl's Algebra in Noncommutative Space
Zhang, J Z
2006-01-01
An extensively tacit understandings of equivalency between the deformed Heisenberg-Weyl algebra in noncommutative space and the undeformed Heisenberg-Weyl algebra in commutative space is elucidated. Equivalency conditions between two algebras are clarified. It is explored that the deformed algebra related to the undeformed one by a non-orthogonal similarity transformation. Furthermore, non-existence of a unitary similarity transformation which transforms the deformed algebra to the undeformed one is demonstrated. The un-equivalency theorem between the deformed and the undeformed algebras is fully proved. Elucidation of this un-equivalency theorem has basic meaning both in theory and practice.
Emergent Power-Law Phase in the 2D Heisenberg Windmill Antiferromagnet: A Computational Experiment.
Jeevanesan, Bhilahari; Chandra, Premala; Coleman, Piers; Orth, Peter P
2015-10-23
In an extensive computational experiment, we test Polyakov's conjecture that under certain circumstances an isotropic Heisenberg model can develop algebraic spin correlations. We demonstrate the emergence of a multispin U(1) order parameter in a Heisenberg antiferromagnet on interpenetrating honeycomb and triangular lattices. The correlations of this relative phase angle are observed to decay algebraically at intermediate temperatures in an extended critical phase. Using finite-size scaling we show that both phase transitions are of the Berezinskii-Kosterlitz-Thouless type, and at lower temperatures we find long-range Z(6) order.
Weyl-Heisenberg frames, translation invariant systems, and the Walnut representation
DEFF Research Database (Denmark)
Casazza, P.G.; Christensen, Ole; Janssen, A. J. E. M.
2001-01-01
We present a comprehensive analysis of the convergence properties of the frame operators of Weyl-Heisenberg systems and shift-invariant systems, and relate these to the convergence of the Walnut representation. We give a deep analysis of necessary conditions and sufficient conditions for converge......We present a comprehensive analysis of the convergence properties of the frame operators of Weyl-Heisenberg systems and shift-invariant systems, and relate these to the convergence of the Walnut representation. We give a deep analysis of necessary conditions and sufficient conditions...
Critical behavior of the three-dimensional Heisenberg antiferromagnet RbMnF3
DEFF Research Database (Denmark)
Coldea, R.; Cowley, R.A.; Perring, T.G.;
1998-01-01
The magnetic critical scattering of the near-ideal three-dimensional Heisenberg antiferromagnet (AF) RbMnF3 has been remeasured using neutron scattering. The critical dynamics has been studied in detail in the temperature range 0.77T(N) < T < 1.11T(N), where T-N is the Neel temperature. In agreem......The magnetic critical scattering of the near-ideal three-dimensional Heisenberg antiferromagnet (AF) RbMnF3 has been remeasured using neutron scattering. The critical dynamics has been studied in detail in the temperature range 0.77T(N)
Critical behavior of the Heisenberg ferromagnets EuO and EuS
DEFF Research Database (Denmark)
Als-Nielsen, Jens Aage; Dietrich, O.W.; Kunnmann, W.;
1971-01-01
Neutron-scattering measurements have been made of the critical parameters of the simple Heisenberg ferromagnets EuO and EuS. Values of the critical exponents β and ν and the amplitudes of B and F describing, respectively, the reduced magnetization and the inverse correlation range (above Tc......) are in good accord with theory. The measured values of the exponent γ, describing the static susceptibility, support the recent prediction that γ≈1.40 in a simple nearest-neighbor Heisenberg ferromagnet. The scaling relation between β, ν, and γ is fulfilled...
Yao, Xiaoyan; Dong, Shuai
2016-05-27
The expanded classical Kitaev-Heisenberg model on a honeycomb lattice is investigated with the next-nearest-neighboring Heisenberg interaction considered. The simulation shows a rich phase diagram with periodic behavior in a wide parameter range. Beside the double 120° ordered phase, an inhomogeneous phase is uncovered to exhibit a topological triple-vortex lattice, corresponding to the hexagonal domain structure of vector chirality, which is stabilized by the mixed frustration of two sources: the geometrical frustration arising from the lattice structure as well as the frustration from the Kitaev couplings.
Long-range order for the spin-1 Heisenberg model with a small antiferromagnetic interaction
Energy Technology Data Exchange (ETDEWEB)
Lees, Benjamin, E-mail: b.lees@warwick.ac.uk [Department of Mathematics, University of Warwick, Coventry CV4 7AL (United Kingdom)
2014-09-15
We look at the general SU(2) invariant spin-1 Heisenberg model. This family includes the well-known Heisenberg ferromagnet and antiferromagnet as well as the interesting nematic (biquadratic) and the largely mysterious staggered-nematic interaction. Long range order is proved using the method of reflection positivity and infrared bounds on a purely nematic interaction. This is achieved through the use of a type of matrix representation of the interaction making clear several identities that would not otherwise be noticed. Using the reflection positivity of the antiferromagnetic interaction one can then show that the result is maintained if we also include an antiferromagnetic interaction that is sufficiently small.
Quantization of the inhomogeneous Bianchi I model: quasi-Heisenberg picture
Cherkas, S L
2013-01-01
The quantization scheme is suggested for a spatially inhomogeneous 1+1 Bianchi I model. The scheme consists in quantization of the equations of motion and gives the operator (so-called quasi-Heisenberg) equations describing an explicit evolution of a system. Some particular gauge suitable for quantization is proposed. The Wheeler-DeWitt equation is considered in the vicinity of zero scale factor and it is used to construct a space, where the quasi-Heisenberg operators act. Spatial discretization as a UV regularization procedure is suggested for the equations of motion.
Directory of Open Access Journals (Sweden)
Jialin Wang
2013-01-01
Full Text Available This paper is concerned with partial regularity to nonlinear subelliptic systems with Dini continuous coefficients under quadratic controllable growth conditions in the Heisenberg group ℍn. Based on a generalization of the technique of -harmonic approximation introduced by Duzaar and Steffen, partial regularity to the sub-elliptic system is established in the Heisenberg group. Our result is optimal in the sense that in the case of Hölder continuous coefficients we establish the optimal Hölder exponent for the horizontal gradients of the weak solution on its regular set.
Self-Duality Helicity and Higher-Loop Euler-Heisenberg Effective Actions
Dunne, Gerald V.; Schubert, Christian
2004-10-01
The Euler-Heisenberg effective action in a self-dual background is remarkably simple at two-loop. This simplicity is due to the inter-relationship between self-duality, helicity and supersymmetry. Applications include two-loop helicity amplitudes, beta-functions and nonperturbative effects. The two-loop Euler-Heisenberg effective Lagrangian for QED in a self-dual background field is naturally expressed in terms of one-loop quantities. This mirrors similar behavior recently found in two-loop amplitudes in N=4 SUSY Yang-Mills theory.
Monte Carlo simulation of Prussian blue analogs described by Heisenberg ternary alloy model
Yüksel, Yusuf
2015-11-01
Within the framework of Monte Carlo simulation technique, we simulate magnetic behavior of Prussian blue analogs based on Heisenberg ternary alloy model. We present phase diagrams in various parameter spaces, and we compare some of our results with those based on Ising counterparts. We clarify the variations of transition temperature and compensation phenomenon with mixing ratio of magnetic ions, exchange interactions, and exchange anisotropy in the present ferro-ferrimagnetic Heisenberg system. According to our results, thermal variation of the total magnetization curves may exhibit N, L, P, Q, R type behaviors based on the Néel classification scheme.
Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench.
Barmettler, Peter; Punk, Matthias; Gritsev, Vladimir; Demler, Eugene; Altman, Ehud
2009-04-03
We study the unitary time evolution of antiferromagnetic order in anisotropic Heisenberg chains that are initially prepared in a pure quantum state far from equilibrium. Our analysis indicates that the antiferromagnetic order imprinted in the initial state vanishes exponentially. Depending on the anisotropy parameter, oscillatory or nonoscillatory relaxation dynamics is observed. Furthermore, the corresponding relaxation time exhibits a minimum at the critical point, in contrast to the usual notion of critical slowing down, from which a maximum is expected.
Low-temperature study of the magnetic properties of finite atomic chains
Kolesnikov, S. V.
2016-05-01
A simple method for the calculation of the spontaneous remagnetization time and magnetization curves of atomic finite-length ferromagnetic chains at a low temperature within the Heisenberg model has been proposed. The applicability limits of the method have been studied. It has been shown that the proposed method gives results being in good agreement with the kinetic Monte Carlo simulation results. Formulas obtained within our model can also be used to determine the lower bound for the Curie temperature.
THERMODYNAMIC PROPERTIES OF LADDER--LIKE HEISENBERG SYSTEM
Institute of Scientific and Technical Information of China (English)
蒋青; 潘可扬
1993-01-01
By combining the cumulant expansion method with the double-chain approximation, we study thermodynamic properties of ladder-like He isenberg system. We find the interaction between interchains has different effect in high and low temperature.
Sadri, D; Sadri, Darius
2006-01-01
We consider $N=1, D=4$ superconformal $U(N)^{pq}$ Yang-Mills theories dual to AdS_5xS^5/Z_pxZ_q orbifolds. We construct the dilatation operator of this superconformal gauge theory at one-loop planar level. We demonstrate that a specific sector of this dilatation operator can be thought of as the transfer matrix for a two-dimensional statistical mechanical system, related to an integrable SU(3) anti-ferromagnetic spin chain system, which in turn is equivalent to a 2+1-dimensional string theory where the spatial slices are discretized on a triangular lattice. This is an extension of the SO(6) spin chain picture of N=4 super Yang-Mills theory. We comment on the integrability of this N=1 gauge theory and hence the corresponding three-dimensional statistical mechanical system, its connection to three-dimensional lattice gauge theories, extensions to six-dimensional string theories, AdS/CFT type dualities and finally their construction via orbifolds and brane-box models. In the process we discover a new class of al...
Zad, Hamid Arian; Movahhedian, Hossein
2016-08-01
Heat capacity of a mixed-three-spin (1/2,1,1/2) antiferromagnetic XXX Heisenberg chain is precisely investigated by use of the partition function of the system for which, spins (1,1/2) have coupling constant J1 and spins (1/2,1/2) have coupling constant J2. We verify tripartite entanglement for the model by means of the convex roof extended negativity (CREN) and concurrence as functions of temperature T, homogeneous magnetic field B and the coupling constants J1 and J2. As shown in our previous work, [H. A. Zad, Chin. Phys. B 25 (2016) 030303.] the temperature, the magnetic field and the coupling constants dependences of the heat capacity for such spin system have different behaviors for the entangled and separable states, hence, we did some useful comparisons between this quantity and negativities of its organized bipartite (sub)systems at entangled and separable states. Here, we compare the heat capacity of the mixed-three-spin (1/2,1,1/2) system with the CREN and the tripartite concurrence (as measures of the tripartite entanglement) at low temperature. Ground state phase transitions, and also, transition from ground state to some excited states are explained in detail for this system at zero temperature. Finally, we investigate the heat capacity behavior around those critical points in which these quantum phase transitions occur.
Werner Heisenberg and the German Uranium Project 1939 - 1945. Myths and Facts
Gottstein, Klaus
2016-01-01
The results of a careful analysis of all the available information on the activities of Heisenberg and of his talks during the years 1939 to 1945 can be summarized in the following way. Like several other German physicists Heisenberg was drafted by German Army Ordnance when war began in Europe in September 1939 to investigate whether the energy from splitting Uranium nuclei by neutrons could be used for technical and military purposes. Heisenberg found that this is possible in principle but that military use would require such enormous industrial expenditures that it would take many years and would be impracticable while the war lasted. The project was therefore dropped by the Nazi government in 1942. Heisenberg even refrained from calculating a precise value for the critical mass of U 235. He was relieved that he was thus spared a moral decision between obeying an order to build the bomb or risking his life by refusing to be involved in the project or sabotaging it. He was happy to be confined to a project o...
Deformed C λ-Extended Heisenberg Algebra in Noncommutative Phase-Space
Douari, Jamila
2006-05-01
We construct a deformed C λ-extended Heisenberg algebra in two-dimensional space using noncommuting coordinates which close an algebra depends on statistical parameter characterizing exotic particles. The obtained symmetry is nothing but an exotic particles algebra interpolating between bosonic and deformed fermionic algebras.
While Heisenberg Is Not Looking: The Strength of "Weak Measurements" in Educational Research
Geelan, David R.
2015-01-01
The concept of "weak measurements" in quantum physics is a way of "cheating" the Uncertainty Principle. Heisenberg stated (and 85 years of experiments have demonstrated) that it is impossible to know both the position and momentum of a particle with arbitrary precision. More precise measurements of one decrease the precision…
Exact Results for Spin-Wave Renormalisation in Heisenberg and Planar Ferromagnets
DEFF Research Database (Denmark)
Rastelli, E.; Lindgård, Per-Anker
1979-01-01
An exact perturbation expansion, to the order 1/S2, is derived for the Heisenberg ferromagnet. The equivalence of the Dyson-Maleev (DM), Holstein-Primakoff (HP) and matching-of-matrix-element (MME) transformations is proven. They give identical T5/2 and T4 coefficients. For the planar ferromagnet...
Isotropic non-Heisenberg terms in the magnetic coupling of transition metal complexes.
Bastardis, Roland; Guihéry, Nathalie; de Graaf, Coen
2008-09-14
This paper analyzes the different contributions to the magnetic coupling in systems with more than one unpaired electron per center. While in S=12 spin systems the Heisenberg Hamiltonian involving only bilinear exchange interactions is reliable for the description of the magnetic states, biquadratic exchange interactions must be sometimes introduced for S=1 (or higher) spin systems to account for isotropic deviations to Heisenberg behavior. The analysis establishes that the excited atomic states, the so-called non-Hund states, are responsible for the main contribution to the deviations. The kinetic exchange contribution and the spin, hole, and particle polarizations increase the magnetic coupling but essentially maintain the Heisenberg pattern. The importance of the different contributions has been studied for a series of Ni(2) compounds with a polarizable double azido bridge. The coupling between two Fe(3+) ions in the molecular crystal Na(3)FeS(3), which is known experimentally to present large deviations to Heisenberg behavior, has also been investigated.