Thermal form-factor approach to dynamical correlation functions of integrable lattice models

TL;DR

This paper introduces a novel method for computing finite-temperature dynamical correlation functions in integrable lattice models, utilizing a form-factor series expansion based on a quantum transfer matrix approach.

Contribution

It presents a new thermal form-factor approach that replaces Hamiltonian-based expansions with a transfer matrix framework for dynamical correlations.

Findings

Derived a series representation for dynamical correlations in the XXZ model.

Applied the method to the XX model, obtaining a new form-factor series.

Demonstrated the approach's effectiveness through explicit calculations.

Abstract

We propose a method for calculating dynamical correlation functions at finite temperature in integrable lattice models of Yang-Baxter type. The method is based on an expansion of the correlation functions as a series over matrix elements of a time-dependent quantum transfer matrix rather than the Hamiltonian. In the infinite Trotter-number limit the matrix elements become time independent and turn into the thermal form factors studied previously in the context of static correlation functions. We make this explicit with the example of the XXZ model. We show how the form factors can be summed utilizing certain auxiliary functions solving finite sets of nonlinear integral equations. The case of the XX model is worked out in more detail leading to a novel form-factor series representation of the dynamical transverse two-point function.