XXZ Heisenberg Chain Research Articles

Lattice versus continuum theory of the periodic Heisenberg chain

We consider the detailed structure of low energy excitations in the periodic spin-1/2 XXZ Heisenberg chain. By performing a perturbative calculation of the non-linear corrections to the Gaussian model, we determine the exact coefficients of asymptotic expansions in inverse powers of the system length N for a large number of low-lying excited energy levels. This allows us to calculate eigenenergies of the lattice model up to order order N^-4, without having to solve the Bethe Ansatz equations. At the same time, it is possible to express the exact eigenstates of the lattice model in terms of bosonic modes.

Bipartite entanglement in a two-qubit Heisenberg XXZ chain under an inhomogeneous magnetic field

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.

Effects of inhomogeneous magnetic field on entanglement and teleportation in a two-qubit Heisenberg XXZ chain with intrinsic decoherence

We studied the effects of inhomogeneous magnetic field on entanglement and teleportation in a two-qubit Heisenberg XXZ chain with intrinsic decoherence taken into account. The dependences of the entanglement and fully entangled fraction on the inhomogeneous magnetic fields b and time t are investigated in detail. The contrast between different initial states, including pure and mixed states, is presented.

Teleportation via thermally entangled states of a two-qubit Heisenberg XXZ chain**Supported by Natural Science Research Project of Shaanxi Province (2004A15)

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.

Quantum Teleportation Through a Two-Qubit Heisenberg XXZ Chain

We consider a two-qubit Heisenberg XXZ chain as a resource for quantum teleportation via the standard teleportation protocol T0. The effects of anisotropic on teleportation fidelity and entanglement are studied in detail. We find anisotropic not only improves the critical temperature Tc and critical magnetic field Bc, beyond which quantum teleportation is inferior to classical communication protocol, but also enhances the fidelity for fixed magnetic field B and temperature T. For entanglement teleportation, the effects of magnetic field on average fidelity and output entanglement are studied.

Quantum teleportation via a two-qubit Heisenberg XXZ chain – effects of anisotropy and magnetic field

We study quantum teleportation via a two-qubit Heisenberg XXZ chain under an inhomogeneous magnetic field. We first consider entanglement teleportation, and then focus on the teleportation fidelity under different conditions. The effects of anisotropy and the magnetic field, both uniform and inhomogeneous, are discussed. We also find that, though entanglement teleportation does require an entangled quantum channel, a nonzero critical value of minimum entanglement is not always necessary.

Density matrix elements and entanglement entropy for the spin-1/2 XXZ chain at Δ = 1/2

We have analytically obtained all the density matrix elements up to six lattice sites for the spin-1/2 Heisenberg XXZ chain at Δ = 1/2. We use the multiple integral formula of the correlation function for the massless XXZ chain derived by Jimbo and Miwa. As for the spin–spin correlation functions, we have newly obtained the fourth- and fifth-neighbour transverse correlation functions. We have calculated all the eigenvalues of the density matrix and analyse the eigenvalue distribution. Using these results the exact values of the entanglement entropy for the reduced density matrix up to six lattice sites have been obtained. We observe that our exact results agree quite well with the asymptotic formula predicted by the conformal field theory.

Dynamical correlation functions of the XXZ model at finite temperature

Combining a lattice path integral formulation for thermodynamics with the solution of the quantum inverse scattering problem for local spin operators, we derive a multiple integral representation for the time-dependent longitudinal correlation function of the spin-1/2 Heisenberg XXZ chain at finite temperature and in an external magnetic field. Our formula reproduces the previous results in the following three limits: the static, the zero-temperature and the XY limits.

Thermal Entanglement of XXZ Heisenberg Chain under Rectangle Magnetic Field

We study thermal entanglement of XXZ Heisenberg chain under rectangle magnetic field. Under this magnetic field B, the region of thermal entanglement in terms of B and temperature T can be extended. Moreover, one can improve threshold temperature, where entanglement vanish, just by increasing the strength of magnetic field. This effect is similar to that of the anisotropic coupling of spin in XY plane but provide us a realizable method to improve threshold temperature.

String correlation functions of the spin-1/2 Heisenberg XXZ chain

We calculate certain string correlation functions, originally introduced as order parameters in integer spin chains, for the spin-1/2 XXZ Heisenberg chain at zero temperature and in the thermodynamic limit. For small distances, we obtain exact results from Bethe Ansatz and exact diagonalization, whereas in the large-distance limit, field-theoretical arguments yield an asymptotic algebraic decay. We also make contact with two-point spin-correlation functions in the asymptotic limit.

Correlation functions of the XXZ Heisenberg chain for Δ = 1/2

We present exact results for the correlation functions of the XXZ Heisenberg chain in the thermodynamic limit for the anisotropy parameter Δ = 1/2. We show that the results are given by integers.

A note on the high temperature expansion of the density matrix for the isotropic Heisenberg chain

Göhmann, Klümper and Seel derived the multiple integral formula of the density matrix of the XXZ Heisenberg chain at finite temperatures. We have applied the high temperature expansion (HTE) method to isotropic case of their formula in a finite magnetic field and obtained coefficients for several short-range correlation functions. For example, we have succeeded to obtain the coefficients of the HTE of the third neighbor correlation function 〈 σ j z σ j + 3 z 〉 for zero magnetic field up to the order of 25. These results expand our previous results on the emptiness formation probability [Z. Tsuboi, M. Shiroishi, J. Phys. A: Math. Gen. 38 (2005) L363–L370, condmat/0502569.] to more general correlation functions.

Effects of Anisotropy on Pair-wise Entanglement of a Four-QubitHeisenberg XXZ Chain

The pair-wise thermal entanglement in a four-qubit Heisenberg XXZchain is investigated to study the role of anisotropy when anexternal magnetic field is included. It is found that pair-wiseentanglement is absent between nearest- and next-nearest neighbouringqubits with anisotropic parameter Δ⩽−1. For twonearest-neighbouring qubits, increasing the parameter can not onlyinduce the entanglement, but also extend the entanglement region interms of magnetic field B and temperature T. For twonext-nearest-neighbouring qubits, increasing anisotropic parameter canshift the location of the entanglement and control the extent of theentanglement in terms of magnetic field at a finite temperature.

Magnetization plateau in the spin ladder with alternating rung exchange

We have studied the ground-state phase diagram of a spin ladder with alternating rungexchange in a magnetic filed, in the limit where the rung coupling is dominant. In this limit the model is mappedonto an XXZ Heisenberg chain in uniform and staggered longitudinal magnetic fields, where the amplitude of the staggeredfield is ∼δ. We have shown that the magnetization curve of the system exhibits a plateau atmagnetization equal to half of the saturation value. The width of a plateau scales asδν,where ν = 4/5 in the case of a ladder with isotropic antiferromagnetic legs andν = 2 in the case of a ladder with isotropic ferromagnetic legs. We have calculated four critical fields(Hc1 ± and Hc2 ± ) corresponding to transitions between different magnetic phases of the system.We have shown that these transitions belong to the universality class of thecommensurate–incommensurate transition. The possibility for the realization of a new typeof spin-Peierls instability, characterized by the spontaneous appearance of an alternatingrung exchange in a uniform magnetic field and at a system magnetization equal to the halfof its saturation value, is briefly discussed.

Thermomagnetic Power and Figure of Merit for Spin-1/2 Heisenberg Chain

Transport properties in the presence of magnetic fields are numerically studied for the spin-1/2 Heisenberg XXZ chain. The breakdown of the spin-reversal symmetry due to the magnetic field induces the magnetothermal effect. In analogy with the thermoelectric effect in electron systems, the thermomagnetic power (magnetic Seebeck coefficient) is provided, and is numerically evaluated by the exact diagonalization for wide ranges of temperatures and various magnetic fields. For the antiferromagnetic regime, we find the magnetic Seebeck coefficient changes sign at certain temperatures, which is interpreted as an effect of strong correlations. We also compute the thermomagnetic figure of merit determining the efficiency of the thermomagnetic devices for cooling or power generation.

Anomalous magnetothermal effect in the spin- [formula omitted] Heisenberg XXZ chain

The low-temperature thermomagnetic power of the spin- 1 2 Heisenberg XXZ chain is exactly calculated by the Bethe ansatz. For finite magnetic fields, the magnetothermal effects arise due to the breakdown of the spin-reversal symmetry. For finite interaction strengths, we find the thermomagnetic coefficient (magnetic Seebeck coefficient) changes sign at certain temperature and magnetic field. This peculiar feature is interpreted as an effect of the competition between the interaction strength and the external magnetic field.

Exact Ground State and Finite-Size Scaling in a Supersymmetric Lattice Model

We study a model of strongly correlated fermions in one dimension with extended N = 2 supersymmetry. The model is related to the spin S = 1/2 XXZ Heisenberg chain at anisotropy Delta = -1/2 with a real magnetic field on the boundary. We exploit the combinatorial properties of the ground state to determine its exact wave function on finite lattices with up to 30 sites. We compute several correlation functions of the fermionic and spin fields. We discuss the continuum limit by constructing lattice observables with well defined finite-size scaling behavior. For the fermionic model with periodic boundary conditions we give the emptiness formation probability in closed form.

Formula omitted] contribution of saddle point fluctuations to the free energy of Bethe Ansatz systems

We develop a method to calculate the contribution of the saddle-point fluctuations to the partition function of systems soluble by the Bethe Ansatz. Using this method we give the O ( 1 ) corrections to the free energy of the 1D repulsive δ Bose gas both for periodic boundary conditions and for the open end case. We also generalize our method to more complicated systems and discuss the case of XXZ Heisenberg chain in more details.

Emptiness Formation Probability in the Spin-1/2 XXZ Heisenberg Chain

We present several explicit results for the emptiness formation probability in the spin-1/2 XXZ Heisenberg chain. We obtain these results using new integral representations for the correlation functions.

Limit temperature for entanglement in generalized statistics

We discuss the main properties of general thermal states derived from non-additive entropic forms and their use for studying quantum entanglement. It is shown that all these states become more mixed as the temperature increases, approaching the full random state for T→∞. The formalism is then applied to examine the limit temperature for entanglement in a two-qubit XXZ Heisenberg chain, which exhibits the peculiar feature of being independent of the applied magnetic field in the conventional von Neumann based statistics. In contrast, this temperature is shown to be field dependent in a generalized statistics, even for small deviations from the standard form. Results for the Tsallis-based statistics are examined in detail.