Thermal form factors of the XXZ chain and the large-distance asymptotics of its temperature dependent correlation functions

TL;DR

This paper derives explicit form factor formulas for the XXZ chain's temperature-dependent correlation functions, enabling precise asymptotic analysis at large distances and temperatures, and confirms conformal field theory predictions.

Contribution

The authors develop novel form factor expressions suitable for the infinite Trotter limit, facilitating detailed asymptotic analysis of finite-temperature correlations in the XXZ chain.

Findings

Explicit large-distance asymptotics for longitudinal two-point functions at low temperatures.

Validation of conformal field theory predictions through direct calculation.

Effective summation of dominant form factors in high- and low-temperature regimes.

Abstract

We derive expressions for the form factors of the quantum transfer matrix of the spin-1/2 XXZ chain which are suitable for taking the infinite Trotter number limit. These form factors determine the finitely many amplitudes in the leading asymptotics of the finite-temperature correlation functions of the model. We consider form-factor expansions of the longitudinal and transversal two-point functions. Remarkably, the formulae for the amplitudes are in both cases of the same form. We also explain how to adapt our formulae to the description of ground state correlation functions of the finite chain. The usefulness of our novel formulae is demonstrated by working out explicit results in the high- and low-temperature limits. We obtain, in particular, the large-distance asymptotics of the longitudinal two-point functions for small temperatures by summing up the asymptotically most relevant terms in the form factor expansion of a generating function of the longitudinal correlation functions. As expected the leading term in the expansion of the corresponding two-point functions is in accordance with conformal field theory predictions. Here it is obtained for the first time by a direct calculation.