Quantum topological excitations: from the sawtooth lattice to the Heisenberg chain

From the recently determined structure of the delafossite YCuO_2.5, we argue that the Cu-O network has nearly independent Δ chains but with different interactions between the s = 1/2 spins. Motivated by this observation, we study the Δ chain for different ratios of the base-base and base-vertex interactions, J _bb/J _bv. By exact diagonalization and extrapolation, we show that the elementary excitation spectrum is the same for total spins S _tot = 0 and 1, but not for S _tot = 2, and has a gap only in the interval 0.4874(1) ⩽ J _bb/J _bv ⩽ 1.53(1). The gap, known to be dispersionless for J _bb = J _bv, is found to acquire increasing k-dependence as J _bb/J _bv moves away from unity. Received 29 October 2002 / Received in final form 14 January 2003 Published online 6 March 2003 RID="a" ID="a"e-mail: sblundell@cea.fr RID="b" ID="b"e-mail: nunezreg@lps.u-psud.fr     

Thermal entanglement of the Ising Heisenberg diamond chain with Dzyaloshinskii Moriya interaction

We investigate the thermal entanglement in a spin-1/2 Ising–Heisenberg diamond chain, in which the vertical Heisenberg spin dimers alternate with single Ising spins. Due to the fact that the Dzyaloshinskii–Moriya(DM) interaction contributes 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 D z 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 interaction, thus DM interaction favors the formation of the thermal entanglement. It is observed that different DM interaction parameters(Dz and Dx) have remarkably different influences 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.     

Vitrification in a 2D Ising model with mobile bonds

A bond-disordered two-dimensional Ising model is used to simulate Kauzmann's mechanism of vitrification in liquids, by a Glauber Monte Carlo simulation. The rearrangement of configurations is achieved by allowing impurity bonds to hop to nearest neighbors at the same rate as the spins flip. For slow cooling, the theoretical minimum energy configuration is approached, characterized by an amorphous distribution of locally optimally arranged impurity bonds. Rapid cooling to low temperatures regularly finds bond configurations of higher energy, which are both a priori rare and severely restrictive to spin movement, providing a simple realization of kinetic vitrification. A supercooled liquid regime is also found, and characterized by a change in sign of the field derivative of the spin-glass susceptibility at a finite temperature. Received 3 August 2000 and Received in final form 9 March 2001     

Ising phases of Heisenberg ladders in a magnetic field

We show that Dzyaloshinskii-Moriya (DM) interactions can substantially modify the phase diagram of spin-1/2 Heisenberg ladders in a magnetic field provided they compete with exchange. For nonfrustrated ladders, they induce a local magnetization along the DM vector that turns the gapless intermediate phase into an Ising phase with broken translational symmetry, while for frustrated ladders, they extend the Ising order of the half-integer plateau to the surrounding gapless phases of the purely Heisenberg case. Implications for experimental ladder and dimer systems are discussed.     

Decorated Ising Square Lattice in a Magnetic Field

Physics of the Solid State - The Ising model on a decorated square lattice with various parameters of exchange interactions in an external magnetic field is studied. A comparison is made with the...     

Lattice distortions in terbium chalcogenides and pnictides

The temperature dependence of the trigonal lattice distortion in TbS, TbSe, TbTe and TbBi is reported. Below the Néel point the rocksalt cell is rhombohedrally elongated in agreement with the moment orientation in these type II antiferromagnets. In the Tb chalcogenides as well as in TbBi the phase transition appears to be of second order.     

Coarsening in a driven Ising chain with conserved dynamics

We study the low-temperature coarsening of an Ising chain subject to spin-exchange dynamics and a small driving force. This dynamical system reduces to a domain diffusion process, in which entire domains undergo nearest-neighbor hopping, except for the shortest domains-dimers-which undergo long-range hopping. This system exhibits anomalous ordering dynamics due to the existence of two characteristic length scales: the average domain length L(t) approximately t(1/2) and the average dimer hopping distance l(t) approximately square root[L(t)] approximately t(1/4). As a consequence of these two scales, the density of short domains decays as t(-5/4), instead of the t(-3/2) decay that would arise from pure domain diffusion.     

Lattice distortions due to deuterium in niobium

The quasielastic diffuse scattering of neutrons from deuterium interstitials in niobium has been measured and compared to data calculated from a Kanzaki force model with central forces acting on nearest and next-nearest neighbours. It is found that the cubic symmetry of the long range distortion field of H in Nb is already established in the immediate neighbourhood of the defect.     

Ferromagnetic Heisenberg spin chain in a resonator

We investigate the properties of a generalized Rabi model by replacing the two-level atom in Rabi model with a ferromagnetic Heisenberg spin chain. We find that the dynamical behavior of the system can be divided into four categories.The energy spectrum of the ground state and some low excited states are obtained. When the magnons and the photon are in resonance, the model is exactly solvable and the rigorous solution is obtained. Near the resonance point where the detuning is small, the system is studied with the help of perturbation theory. This model has a spontaneously breaking of parity symmetry, suggesting the existence of a quantum phase transition. The critical exponent from the normal phase is computed.     

Many-Body Localization Transition in the Heisenberg Ising Chain

In this paper, we use exact matrix diagonalization to explore the many-body localization (MBL) transition of the Heisenberg Ising spin-1/2 chain with nearest neighbor couplings and disordered external fields. It demonstrates that the fidelity, magnetization and spin-spin space correlation can be used to characterize the many-body localization transition in this closed spin system which is also in agreement with previous analytical and numerical results. We test the properties for the middle third many-body eigenstates. It shows that for this model with random-field, the excited-state fidelity exhibits a pronounced drop at the transition and then gradually tends to be stable in the localized phase, the critical point and the final value of averaged fidelity are all size dependent. It demonstrates that disordered external fields drive the occurrence of the MBL transition. Moreover, we investigate the magnetization and spin-spin space correlation in this model to verify the conclusion we got and further explore the properties of ergodic phase and localized phase.

     

On the magnetically dilute Heisenberg and Ising ferromagnetics

The dependence of Curie point, θ _c, on magnetic concentration, p, is investigated, for the randomly dilute ferromagnetic Heisenberg spin 1/2 problem, by considering successive approximations to 1/χ=0, where χ is the susceptibility. This extends to the next approximation work previously reported by the authors. The simple cubic and body-centred cubic lattices are dealt with in detail. It is concluded that the behaviour of θ _c(p) for small p is not yet fully established: it is possible that the critical concentration p _c, below which there is no ferromagnetic behaviour, is greater for the Heisenberg model than for the corresponding Ising model (where it is the analogous site percolation problem critical probability).     

Entanglement dynamics of a Heisenberg chain with Dzyaloshinskii--Moriya interaction

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 Dzyaloshinskii--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.     

Quantum Teleportation via a Two-Qubit Ising Heisenberg Chain with an Arbitrary Magnetic Field

The quantum teleportation via a two-qubit Ising Heisenberg chain in the presence of an external magnetic field with an arbitrary direction are investigated. The effect of the orientation of an external magnetic field on the entanglement teleportation has been analyzed numerically. It is found that the teleported thermal concurrence and average fidelity can be maximized by rotating the magnetic field (with fixed magnitude) to an optimal direction. The ferromagnetic channel is not suitable to teleportation. A minimal entanglement of the thermal state is needed to realize the entanglement teleportation for antiferromagnetic channel. It is also found that the entanglement of the channel cannot completely reflect the teleported concurrence and average fidelity. There exist double-value phenomena between them.     

Spin-glass transition in bond-disordered Heisenberg antiferromagnets coupled with local lattice distortions on a pyrochlore lattice

Motivated by puzzling characteristics of spin-glass transitions widely observed in pyrochlore-based frustrated materials, we investigate the effects of coupling to local lattice distortions in a bond-disordered antiferromagnet on the pyrochlore lattice by extensive Monte Carlo simulations. We show that the spin-glass transition temperature T(f) is largely enhanced by the spin-lattice coupling and, furthermore, becomes almost independent of Δ in a wide range of the disorder strength Δ. The critical property of the spin-glass transition is indistinguishable from that of the canonical Heisenberg spin glass in the entire range of Δ. These peculiar behaviors are ascribed to a modification of the degenerate manifold from a continuous to semidiscrete one by spin-lattice coupling.     

Quantum breathers in a finite Heisenberg spin chain with antisymmetric interactions

A study of the likelihood of quantum breathers in a quantum Heisenberg spin system including a Dzyaloshinsky-Moriya interaction (DMI) is done through an extended Bose-Hubbard model while using the scheme of few body physics. The energy spectrum of the resulting Bose-Hubbard Hamiltonian, on a periodic one-dimensional lattice containing more than two quanta shows interesting detailed band structures. From a non degenerate, and a degenerate perturbation theory in addition to a numerical diagonalization, a careful investigation of these fine structures is set up. The attention is focussed on the effects of various interactions that are; the DMI, the Heisenberg in-plane (X, Y) as well as the out of plane exchange interaction on the energy spectrum of such a system. The outcome displays a possibility of an energy self-compensation in the system. We also computed the weight function of the eigenstates in direct space and in the space of normal modes. From a perturbation theory it is shown that the interaction between the quanta leads to an algebraic localization of the modified extended states in the normal-mode space of the non-interacting system that are coined quantum q-breathers excitations.     

Ferroelectricity in a diatomic Ising chain as investigated by the elastic Ising model

An elastic Ising model for a one-dimensional diatomic spin chain is proposed to explain the ferroelectricity induced by the collinear magnetic order with a low-excited energy state. A statistical theory based on this model is developed to calculate the electrical and magnetic properties of Ca₃CoMnO₆, a typical quasi-one-dimensional diatomic spin chain system. The calculated ferroelectric polarization and dielectric susceptibility show a good agreement with recently reported data on Ca₃Co_2-xMn_xO₆ (x ≈0.96) (Phys. Rev. Lett. 100 047601 (2008)), although the predicted magnetic susceptibility does not coincide well with experiment. We also address the rationality and deficiency of this model by including a first-order correction which improves the consistency between the model and experiment.     

Nonequilibrium response of a disordered Ising chain

The relaxation behaviour of a model disordered system is studied. The model considered is a nearest neighbour Ising chain in which the bond strengths are distributed at random between the discrete values +J and -J with equal probability. The system is prepared in a given state and is allowed to relax to a new state of equilibrium. This approach to equilibrium is probed by means of an applied, weak, time-dependent magnetic field. The relevant physical quantity is a nonequilibrium susceptibility which is calculated exactly. A comparison between this, and the corresponding quantity for the pure chain, reveals certain distinctive features of the time-dependent properties of disordered systems.Deceased