We explore short-distance static correlation functions in the infinite XXZ chain using previously derived formulae which represent the correlation functions in factorized form. We compute two-point functions ranging over 2, 3 and 4 lattice sites as functions of the temperature and the magnetic field in the massive regime $Δ>1$, extending our previous results to the full parameter plane of the antiferromagnetic chain ($Δ> -1$ and arbitrary field $h$). The factorized formulae are numerically efficient and allow for taking the isotropic limit ($Δ= 1$) and the Ising limit ($Δ= \infty$). At the critical field separating the fully polarized phase from the Néel phase, the Ising chain possesses exponentially many ground states. The residual entropy is lifted by quantum fluctuations for large but finite $Δ$ inducing unexpected crossover phenomena in the correlations.
Exactly conserved quasilocal operators for the XXZ spin chain
我们推广了T. Prosen的XXZ模型的准局部守恒量的构造[Phys. Rev. Lett. 106，217206（2011）]到周期性边界条件的情况。这些准局部算子源于一个双参数转移矩阵，它采用了杨-巴克斯特代数中固有的量子群代数的最高权重表示。与开链相比，开链中的拟局部算子与哈密顿量和其它局部守恒量正好可换，而开链中的边界项弱地违反守恒定律.
Taking the Ising chain as a reference model we have derived a perturbative expression for the free energy density of the Heisenberg-Ising chain with strong easy-axis anisotropy. All calculations are performed on the ground of the Quantum Transfer Matrix approach. The obtained result agrees with the direct high-temperature expansion. It also agrees with the low-temperature cluster expansion in the special subregime when quantum fluctuations are weak against thermodynamical ones.
The tripartite information is an observable-independent measure for scrambling and delocalization of information. Therefore one can expect that the tripartite information is a good observable-independent indicator for distinguishing between many-body localized and delocalized regimes, which we confirm for the XXZ-chain in a random field. Specifically, we find that the tripartite information signal spreads inside a lightcone that only grows logarithmically in time in the many-body localized regime similar to the entanglement entropy. We also find that the tripartite information eventually reach…
We study the thermodynamic limit of the antiperiodic XXZ spin chain with the anisotropic parameter $η=\frac{πi}{3}$. We parameterize eigenvalues of the transfer matrix by their zero points instead of Bethe roots. We obtain patterns of the distribution of zero points. Based on them, we calculate the ground state energy and the elementary excitations in the thermodynamic limit. We also obtain the two-body scattering matrix of elementary excitations. Two types of elementary excitations and three types of scattering processes are discussed in detailed.
