Finite-temperature dynamical correlations in massive integrable quantum fieldtheories

Abstract

We consider the finite-temperature frequency and momentum-dependent two-pointfunctions of local operators in integrable quantum field theories. We focus on the casewhere the zero-temperature correlation function is dominated by a delta-function linearising from the coherent propagation of single-particle modes. Our specific examples arethe two-point function of spin fields in the disordered phase of the quantum Ising and theO(3) nonlinear sigma models. We employ a Lehmann representation in terms of the known exactzero-temperature form factors to carry out a low-temperature expansion of two-pointfunctions. We present two different but equivalent methods of regularizing the divergencespresent in the Lehmann expansion: one directly regulates the integral expressions of thesquares of matrix elements in the infinite volume whereas the other operates throughsubtracting divergences in a large, finite volume. Our central results are that thetemperature broadening of the lineshape exhibits a pronounced asymmetry and a shift ofthe maximum upwards in energy (‘temperature-dependent gap’). The field theory resultspresented here describe the scaling limits of the dynamical structure factor in the quantumIsing and integer spin Heisenberg chains. We discuss the relevance of our results for theanalysis of inelastic neutron scattering experiments on gapped spin chain systems such asCsNiCl3 andYBaNiO5.