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We rigorously prove that the S = 1 / 2 anisotropic Heisenberg chain (XYZ chain) with next-nearest-neighbor interaction, which is anticipated to be non-integrable, is indeed non-integrable in the sense that this system has no nontrivial local conserved quantity. Our result covers some important models including the Majumdar–Ghosh model, the Shastry–Sutherland model, and many other zigzag spin chains as special cases. These models are shown to be non-integrable while they have some solvable energy eigenstates. In addition to this result, we provide a pedagogical review of the proof of non-integrability of the S = 1 / 2 XYZ chain with Z magnetic field, whose proof technique is employed in our result. [ABSTRACT FROM AUTHOR]

The pretty good transmission (PGT) scenario implies that the probability of sending one excitation from one extreme of a spin chain to the other can reach values arbitrarily close to the unity just by waiting a time long enough. The conditions that ensure the appearance of this scenario are known for chains with different interactions and lengths. Sufficient conditions for the presence of PGT depend on the spectrum of the Hamiltonian of the spin chain. Some works suggest that the time t ɛ at which the PGT takes place scales as 1 / (| ε | ) f (N) , where ɛ is the difference between the probability that a single excitation propagates from one extreme of the chain to the other and the unity, while f (N) is an unknown function of the chain length. In this paper, we show that the exponent is not a simple function of the chain length but a power law of the number of linearly independent irrational eigenvalues of the one-excitation block of the Hamiltonian that enter into the expression of the probability of transmission of one excitation. We explicitly provide examples of a chain showing that the exponent changes when the couplings between the spins change while the length remains fixed. For centrosymmetric spin chains the exponent is at most N / 2. [ABSTRACT FROM AUTHOR]

We investigate many-body localization in isotropic Heisenberg spin chains with the local exchange parameters being subject to quenched disorder. Such systems incorporate a nonabelian symmetry in their Hamiltonian by invariance under global SU(2)-rotations. Nonabelian symmetries are predicted to hinder the emergence of a many-body localized phase even in the presence of strong disorder. We report on numerical studies using exact diagonalization for chains of common spin length 1 / 2 and 1. The averaged consecutive-gap ratios display a transition compatible with a crossover from an ergodic phase at small disorder strength to an incompletely localized phase at stronger disorder. Studying the sample-to-sample variance of the averaged consecutive-gap ratio, we distinguish this incompletely localized phase from the fully many-body localized phase by its scaling behavior. [ABSTRACT FROM AUTHOR]

This paper investigates the dynamics of two-spin nonlocality generation in a Heisenberg XXX chain with Dzyaloshinskii-Moriya (DM) and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions. We analyze the two-spin nonlocality dynamics by using uncertainty-induced nonlocality, maximal Bell function, and log-negativity. We demonstrate that a separable two-spin Heisenberg XXX chain state, induced by two-spin antiferromagnetic interaction as well as x-component of DM and KSEA interactions, could evolve to maximal two-spin nonlocality state. The ability of preserving the maximal uncertainty-induced nonlocality can be enhanced by increasing the coupling strength of the spin-spin interaction coupling. The hierarchy principle is maintained for the two-spin Bell nonlocality and log-negativity entanglement. The two-spin log-negativity dynamics exhibits the phenomena of sudden death and birth. The sudden-death phenomenon is due to the intrinsic decoherence, which also causes a reduction in the two-spin nonlocality. While the sudden-birth phenomenon is due to two-spin antiferromagnetic interaction as well as x-component of DM and KSEA interactions. The two-spin uncertainty-induced nonlocality is more robust, against the intrinsic decoherence, than the other types of the nonlocality. The results indicate that by boosting the two-spin antiferromagnetic interaction, the produced nonlocality (resulting from the DM and KSEA x-component interactions) can be shielded from the intrinsic decoherence effect. [ABSTRACT FROM AUTHOR]

This study explores the dynamics of the formation of quantum correlations, namely: local quantum Fisher information and concurrence in a two-spin Heisenberg XXX system. The x-direction of Kaplan–Shekhtman–Entin–Wohlman–Aharony (KSEA) and Dzyaloshinskii–Moriya (DM) interactions as well as the intrinsic decoherence are considered. We show that the interactions are responsible of transforming separable states to correlated states. We point out that by strengthening the two-spin antiferromagnetic interaction coupling, it is possible to increase the capacity to develop semi-regularly maximal two-spin correlations. By increasing the DM and KSEA x-components, the two-spin XXX–Heisenberg exalts maximal local Fisher information and concurrence correlations with large amplitudes and high frequencies. As the intrinsic decoherence increases, the amplitudes and frequencies of the correlations decrease, which also causes the phenomena of sudden death–birth and sudden changes of the correlations. The two-spin correlation produced by the unitary x-component interactions can be shielded from the intrinsic decoherence by increasing the two-spin antiferromagnetic interaction coupling.

This article explores the concurrence in a two-qubit Heisenberg XXX model with Dzyaloshinskii–Moriya (DM) and Kaplan–Shekhtman–Entin-Wohlman–Aharony (KSEA) interactions. The concurrence expression was developed using the physical variables connected with the chosen system. Our results indicate that the temperature, the spin coupling constant, the x-components of the DM and KSEA interactions may all play a role in determining the degree of intricacy between states. Additionally, these findings imply that the separability of states is obtained at high-temperature domains or by switching the spin coupling. In contrast, the entanglement of states may be achieved at low temperatures or by using high values of the x-components of the DM and KSEA parameters. Furthermore, the DM and KSEA interactions have an identical effect on the concurrence behaviors at high temperatures. [ABSTRACT FROM AUTHOR]

We investigate many-body localization in isotropic Heisenberg spin chains with the local exchange parameters being subject to quenched disorder. Such systems incorporate a nonabelian symmetry in their Hamiltonian by invariance under global SU(2)-rotations. Nonabelian symmetries are predicted to hinder the emergence of a many-body localized phase even in the presence of strong disorder. We report on numerical studies using exact diagonalization for chains of common spin length $1/2$ and 1. The averaged consecutive-gap ratios display a transition compatible with a crossover from an ergodic phase at small disorder strength to an incompletely localized phase at stronger disorder. Studying the sample-to-sample variance of the averaged consecutive-gap ratio, we distinguish this incompletely localized phase from the fully many-body localized phase by its scaling behavior.

Onsager reaction field theory is used to investigate the one-dimensional ferromagnetic long-range interacting spin chain with the antiferromagnetic nearest-neighbor interaction (NNI) J ̃. The ferromagnetic long-range interactions considered in this paper decay as J / r p with the distance r between lattice sites. It is found that both the zero temperature and finite-temperature phase diagrams of the system are strongly affected by the interplay between ferromagnetic long-range and antiferromagnetic NNIs. The critical temperature and the uniform susceptibility are obtained as a function of α = J ̃ / J and p. At finite temperatures and in the region α < α c (p) in which α c (p) is dependent of p , the ferromagnetic-paramagnetic phase transition survives for 1 < p < 2 and no phase transition exists for p ≥ 2. At α = α c (p) , the ferromagnetic-antiferromagnetic phase transition happens at zero temperature for p > 1. The ground state of the system keeps ferromagnetic when α < α c (p). But for α > α c , the system becomes antiferromagnetic at all temperatures. [ABSTRACT FROM AUTHOR]

We study the effect of magnetic field and temperature on the amount of coherence of two arbitrary spins in the Heisenberg chain. While increasing temperature always leads to lowering the value of this coherence, in case of magnetic field, it increases the coherence up to a certain value and ultimately it decreases its value to zero. Moreover we find that in a Heisenberg chain, at any temperature the coherence between spins vanishes with distance exponentially with a characteristic distance given by ∼ J k T . The effect of magnetic field is only to set the magnitude of this coherence. [ABSTRACT FROM AUTHOR]

We have addressed the specific heat and magnetization of one dimensional spin-1/2 anisotropic antiferromagnetic Heisenberg chain at finite magnetic field. We have investigated the thermodynamic properties by means of excitation spectrum in terms of a hard core Bosonic representation. The effect of in-plane anisotropy thermodynamic properties has also been studied via the Bosonic model by Green's function approach. This anisotropy is considered for exchange constants that couple spin components perpendicular to magnetic field direction. We have found the temperature dependence of the specific heat and longitudinal magnetization in the gapped field induced spin-polarized phase for various magnetic fields and anisotropy parameters. Furthermore we have studied the magnetic field dependence of specific heat and magnetization for various anisotropy parameters. Our results show temperature dependence of specific heat includes a peak so that its temperature position goes to higher temperature with increase of magnetic field. We have found the magnetic field dependence of specific heat shows a monotonic decreasing behavior for various magnetic fields due to increase of energy gap in the excitation spectrum. Also we have studied the temperature dependence of magnetization for different magnetic fields and various anisotropy parameters. [ABSTRACT FROM AUTHOR]

This study explores the dynamics of the formation of quantum correlations, namely: local quantum Fisher information and concurrence in a two-spin Heisenberg XXX system. The x -direction of Kaplan–Shekhtman–Entin–Wohlman–Aharony (KSEA) and Dzyaloshinskii–Moriya (DM) interactions as well as the intrinsic decoherence are considered. We show that the interactions are responsible of transforming separable states to correlated states. We point out that by strengthening the two-spin antiferromagnetic interaction coupling, it is possible to increase the capacity to develop semi-regularly maximal two-spin correlations. By increasing the DM and KSEA x -components, the two-spin XXX–Heisenberg exalts maximal local Fisher information and concurrence correlations with large amplitudes and high frequencies. As the intrinsic decoherence increases, the amplitudes and frequencies of the correlations decrease, which also causes the phenomena of sudden death–birth and sudden changes of the correlations. The two-spin correlation produced by the unitary x -component interactions can be shielded from the intrinsic decoherence by increasing the two-spin antiferromagnetic interaction coupling. • Exploring the quantum correlation dynamics in a two-spinHeisenberg XXX system with the x-direction of Kaplan–Shekhtman–Entin–Wohlman–Aharony and Dzyaloshinskii–Moriya interactions. • By using the intrinsic decoherence model, the study explores the dynamics of the formation of quantum correlations, namely: local quantum Fisher information and concurrence. • The correlations produced by the unitary interactions can be shielded from the intrinsic decoherence by increasing the antiferromagnetic interaction coupling. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the thermal entanglement and teleportation of a thermally mixed entangled via a two-qubit Heisenberg XXX chain with the x-component D x of the Dzyaloshinskii–Moriya interaction. Our findings suggest that temperature T , spin coupling constant J, and the x-components D x may influence entanglement of the output states and, consequently, the possibilities of teleportation protocols. Furthermore, these results indicate that the entanglement of the output states requires a low-temperature regime, weak Dzyaloshinskii–Moriya interaction, or an antiferromagnetic chain. Finally, the channel becomes entangled, making the teleportation protocol conceivable and feasible. • The temperature, spin coupling constant, and the x-components may influence the entanglement of the output states. • The possibilities of teleportation protocols is also influenced by the previous quantities. • The teleportation protocol requires a low-temperature regime, weak Dzyaloshinskii–Moriya interaction, or an antiferromagnetic chain. [ABSTRACT FROM AUTHOR]

We have addressed the static spin conductivity and spin Drude weight of one-dimensional spin-1/2 anisotropic antiferromagnetic Heisenberg chain in the finite magnetic field. We have investigated the behavior of transport properties by means of excitation spectrum in terms of a hard core bosonic representation. The effect of in-plane anisotropy on the spin transport properties has also been studied via the bosonic model by Green's function approach. This anisotropy is considered for exchange constants that couple spin components perpendicular to magnetic field direction. We have found the temperature dependence of the spin conductivity and spin Drude weight in the gapped field induced spin-polarized phase for various magnetic field and anisotropy parameters. Furthermore we have studied the magnetic field dependence of static spin conductivity and Drude weight for various anisotropy parameters. Our results show the regular part of spin conductivity vanishes in isotropic case however Drude weight has a finite non-zero value and the system exhibits ballistic transport properties. We also find the peak in the static spin conductivity factor moves to higher temperature upon increasing the magnetic field at fixed anisotropy. The static spin conductivity is found to be monotonically decreasing with magnetic field due to increase of energy gap in the excitation spectrum. Furthermore we have studied the temperature dependence of spin Drude weight for different magnetic field and various anisotropy parameters. [ABSTRACT FROM AUTHOR]

Entanglement teleportation via two spins coupled to each other by one axis twisting spin squeezing interaction is investigated. We mainly concentrate on the properties of the channel entanglement, the output entanglement and the teleportation fidelity. It shows that the output entanglement increases linearly with increasing the value of the input entanglement. With the increasing of T, the teleportated entanglement increases sharply from zero to a maximum value and then decreases slowly to zero when the temperature is improved to one threshold value of T, and the threshold value of T increases with the increasing of the input entanglement. When enlarging the external magnetic, F firstly decreases quickly to a minimum value as the critical magnetic field Ω is reached, then it increases abruptly to a maximum value and finally it will be a certain value. Besides, the critical external magnetic Ω increases when μ is larger. For Ω<Ω the value of the average fidelity increases with the increasing of μ, but for Ω>Ω the value of it decreases from a maximum value. The influence of T on the average fidelity is similar with μ. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]

The potassium vanadium oxide-fluoride phase β-KVOF3 was prepared by in-situ reduction with hydrothermal methods and characterized by single-crystal X-ray diffraction and magnetic susceptibility measurements. The compound is orthorhombic [space group Pnma, a = 7.1596(2) Å, b = 7.5392(2) Å, c = 13.0506(4) Å, Z = 8]. The material is structurally similar and isoformulaic to d1 materials of formulae AVOF3 ( A+ = alkali metal, ammonium, or organic cation). Magnetic susceptibility data were successfully fit with a Heisenberg chain model. In-situ reduction of V5+ to V4+ during the hydrothermal reaction conditions was observed in the presence of Br- anions. The role of bromide ions in this reduction is explained and employed to reduce a d0 vanadium species to obtain a material with magnetic behavior. [ABSTRACT FROM AUTHOR]

The potassium vanadium oxide-fluoride phase β-KVOF3 was prepared by in-situ reduction with hydrothermal methods and characterized by single-crystal X-ray diffraction and magnetic susceptibility measurements. The compound is orthorhombic [space group Pnma, a = 7.1596(2) Å, b = 7.5392(2) Å, c = 13.0506(4) Å, Z = 8]. The material is structurally similar and isoformulaic to d1 materials of formulae AVOF3 ( A+ = alkali metal, ammonium, or organic cation). Magnetic susceptibility data were successfully fit with a Heisenberg chain model. In-situ reduction of V5+ to V4+ during the hydrothermal reaction conditions was observed in the presence of Br- anions. The role of bromide ions in this reduction is explained and employed to reduce a d0 vanadium species to obtain a material with magnetic behavior. [ABSTRACT FROM AUTHOR]

The anhydrous alum KTi(SO _4 ) _2 , where the Ti ^3+ ( d ^1 , S = 1/2) ions form an anisotropic triangular lattice, has been prepared by a new hydrothermal route and characterized by magnetic susceptibility and neutron scattering measurements. Contrary to expectations, fits to the magnetic susceptibility indicate that the spins are isotropic (i.e. Heisenberg) and that the frustrating couplings are weak; indeed, the system is well modelled by nearly isolated chains. The inelastic neutron scattering data furthermore shows excellent agreement with an exact theoretical calculation for the one-dimensional spinon continuum. The unexpected magnetic properties of KTi(SO _4 ) _2 are explained in the light of density functional calculations, which reveal an unusual orbital ground state for the Ti ^3 + ion.

We propose interconnections between some problems of PDE, geometry, algebra, calculus and physics. Uniqueness of a solution of the Dirichlet problem and of some other boundary value problems for the string equation inside an arbitrary biquadratic algebraic curve is considered. It is shown that a solution is non-unique if and only if a corresponding Poncelet problem for two conics has a periodic trajectory. A set of problems is proven to be equivalent to the above problem. Among them are the solvability problem of the algebraic Pell-Abel equation and the indeterminacy problem of a new moment problem that generalizes the well-known trigonometrical moment problem. Solvability criteria of the above-mentioned problems can be represented in form θ ∈ Q where number θ = m/n is built by means of data for a problem to solve. We also demonstrate close relations of the above-mentioned problems to such problems of modern mathematical physics as elliptic solutions of the Toda chain, static solutions of the classical Heisenberg XY-chain and biorthogonal rational functions on elliptic grids in the theory of the Padé interpolation. [ABSTRACT FROM AUTHOR]

The four site and eight site 1D anti-ferromagnetic Heisenberg chains in the Jordan-Wigner representation are investigated within the standard Hartree-Fock and random phase approximation (RPA) approaches, both in the symmetry unbroken and in the symmetry broken phases. A translation invariant groundstate, obtained by the projection method as a linear combination of a symmetry-broken HF state and its image under reflection, is also considered, for each chain type. It is found that the projection method considerably improves the HF treatment for instance as far as the groundstate energy is concerned, but also with respect to the RPA energies. The results are furthermore confronted with the ones obtained within so-called SCRPA scheme. [ABSTRACT FROM AUTHOR]

We consider the dimerized spin-1/2 Heisenberg chain with spin hexameric distortion of the exchange pattern and study the zero-temperature phase diagram in the parameter space ( J1, J2, J3) by a continuum-limit bosonization approach and the exact diagonalization method. The phase diagram is rich and has two gapped dimer phases. We obtain an estimate of the critical line separating the different gapped dimer phases by the bosonization approach. The existence of the transition line and the difference between dimer phases is checked numerically. The behavior of the energy gap and the dimer order parameter supports the exact location of the gapless line. [ABSTRACT FROM AUTHOR]

Dynamics of the nearest-neighbor concurrence and the block-block entanglement in closed Heisenberg chains with Dzyaloshinskii-Moriya (DM) interactions are simulated numerically. It is found that the nearest-neighbor concurrence and the block-block entanglement can be generated dynamically from an initial antiferromagnetic (AF) state, and DM interactions will enhance the amplitude of oscillation of concurrence and that of block-block entanglement. Furthermore, dynamics of block-block entanglement SL in the chain with even number spins is coincident with the dynamics of SN - L for D = 0. However, with the consideration of DM interactions, the evolution of SL will not be consistent with that of SN - L for the chain with odd number spins. In a given time interval, the maximal value of the generated nearest-neighbor concurrence $C_{i,i+1}^{\max}$ will first decrease with the increase of chain's length, then oscillate with the increase of N. The maximal value and the minimal value of the oscillation becomes stable for a large N, and $C_{i,i+1}^{\max}$ of the chain with odd spins is larger than that of the chain with even spins for a large N. The influence of DM interaction on the value of $C_{i,i+1}^{\max}$ becomes unobvious with the increase of chain's length. [ABSTRACT FROM AUTHOR]