Short-distance thermal correlations in the massive XXZ chain

Abstract

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 ∆ > 1, extending our previous results to the full parameter plane of the antiferromagnetic chain (∆ > −1 and arbitrary field h). The factorized formulae are numerically efficient and allow for taking the isotropic limit (∆ = 1) and the Ising limit (∆ = ∞). 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 ∆ inducing unexpected crossover phenomena in the correlations. *

Exact description of magnetoelectric effect in the spin-12XXZ chain with Dzyaloshinskii-Moriya interaction

“…First of all let us define a basic pair of auxiliary functions as the solution of the nonlinear integral equations, 48 log b(…”

From the sinh-Gordon field theory to the one-dimensional Bose gas: exact local correlations and full counting statistics

“…While integrability directly provides the tools for diagonalizing the Hamiltonian, the computation of correlation functions constitute a remarkable challenge, which has attracted a constant theoretical effort over the past fifty years [2][3][4][5]. Classical studies have in particular focused on ground-state and thermal correlations, and joint efforts have led to spectacular results, for example in the case of prototypical interacting spin models such as the well-known Heisenberg chain [6][7][8][9][10][11][12].More recently, new energy has been pumped into the study of integrable models, also due to the new experimental possibilities offered by cold-atom physics. Nearly ideal integrable systems can now be realized in cold-atom experiments both in and out equilibrium [13][14][15], elevating the relevance of existing works beyond the purely theoretical interest, and motivating further advances in the framework of non-equilibrium physics (see [16] for a collection of recent reviews on this topic).From the experimental point of view, one of the most relevant systems is the so-called Lieb-Liniger (LL) model [17].…”

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