A thermal form factor series for the longitudinal two-point function of the Heisenberg-Ising chain in the antiferromagnetic massive regime

TL;DR

This paper develops a new determinant-based series representation for the longitudinal two-point function of the XXZ spin chain in the antiferromagnetic massive regime, simplifying analysis especially at zero temperature.

Contribution

It introduces a novel form factor series that reduces to finite determinants at zero temperature, improving the analytical tractability of the correlation function.

Findings

Series representation based on form factors of the quantum transfer matrix.

Reduction to a product of two finite determinants at zero temperature.

Facilitates further analysis of the correlation function.

Abstract

We consider the longitudinal dynamical two-point function of the XXZ quantum spin chain in the antiferromagnetic massive regime. It has a series representation based on the form factors of the quantum transfer matrix of the model. The $n$th summand of the series is a multiple integral accounting for all $n$-particle $n$-hole excitations of the quantum transfer matrix. In previous works the expressions for the form factor amplitudes appearing under the integrals were either again represented as multiple integrals or in terms of Fredholm determinants. Here we obtain a representation which reduces, in the zero-temperature limit, essentially to a product of two determinants of finite matrices whose entries are known special functions. This will facilitate the further analysis of the correlation function.