Thermal form factor approach to the ground-state correlation functions of the XXZ chain in the antiferromagnetic massive regime

TL;DR

This paper introduces a new form factor series approach to compute ground-state correlation functions of the XXZ chain in the antiferromagnetic massive regime, offering improved numerical efficiency and insights into temperature effects.

Contribution

It presents novel form factor series representations for the XXZ chain's correlation functions, differing from existing methods and enabling straightforward asymptotic analysis.

Findings

New form factor series representations for the XXZ chain

Numerical efficiency of the new approach

Temperature corrections are negligible in the regime

Abstract

We use the form factors of the quantum transfer matrix in the zero-temperature limit in order to study the two-point ground-state correlation functions of the XXZ chain in the antiferromagnetic massive regime. We obtain novel form factor series representations of the correlation functions which differ from those derived either from the q-vertex-operator approach or from the algebraic Bethe Ansatz approach to the usual transfer matrix. We advocate that our novel representations are numerically more efficient and allow for a straightforward calculation of the large-distance asymptotic behaviour of the two-point functions. Keeping control over the temperature corrections to the two-point functions we see that these are of order $T^\infty$ in the whole antiferromagnetic massive regime. The isotropic limit of our result yields a novel form factor series representation for the two-point correlation functions of the XXX chain at zero magnetic field.