Finite Temperature Dynamical Correlations in Massive Integrable Quantum Field Theories

TL;DR

This paper develops methods to analyze how finite temperature affects dynamical correlations in integrable quantum field theories, revealing asymmetric broadening and energy shifts in spectral lines relevant for experimental spin chain systems.

Contribution

It introduces two regularization techniques for finite-temperature two-point functions and demonstrates their application to specific models, uncovering temperature-induced line shape asymmetry and energy shifts.

Findings

Temperature broadening exhibits pronounced asymmetry.

Maximum of spectral line shifts upwards with temperature.

Results applicable to neutron scattering in gapped spin chains.

Abstract

We consider the finite-temperature frequency and momentum dependent two-point functions of local operators in integrable quantum field theories. We focus on the case where the zero temperature correlation function is dominated by a delta-function line arising from the coherent propagation of single particle modes. Our specific examples are the two-point function of spin fields in the disordered phase of the quantum Ising and the O(3) nonlinear sigma models. We employ a Lehmann representation in terms of the known exact zero-temperature form factors to carry out a low-temperature expansion of two-point functions. We present two different but equivalent methods of regularizing the divergences present in the Lehmann expansion: one directly regulates the integral expressions of the squares of matrix elements in the infinite volume whereas the other operates through subtracting divergences in a large, finite volume. Our central results are that the temperature broadening of the line shape exhibits a pronounced asymmetry and a shift of the maximum upwards in energy ("temperature dependent gap"). The field theory results presented here describe the scaling limits of the dynamical structure factor in the quantum Ising and integer spin Heisenberg chains. We discuss the relevance of our results for the analysis of inelastic neutron scattering experiments on gapped spin chain systems such as CsNiCl3 and YBaNiO5.