One-point functions in integrable quantum field theory at finite temperature

TL;DR

This paper derives a simplified form factor expansion for one-point functions in integrable quantum field theory at finite temperature, clarifying the role of locality and providing low-temperature results for the Ising model in a magnetic field.

Contribution

It presents a new, simpler form factor expansion for finite-temperature one-point functions and clarifies the impact of operator locality on singularities.

Findings

No singularities in local operators' expansions

Divergences in non-local operators linked to symmetry breaking absence

First low-temperature expansion terms for Ising model in magnetic field

Abstract

We determine the form factor expansion of the one-point functions in integrable quantum field theory at finite temperature and find that it is simpler than previously conjectured. We show that no singularities are left in the final expression provided that the operator is local with respect to the particles and argue that the divergences arising in the non-local case are related to the absence of spontaneous symmetry breaking on the cylinder. As a specific application, we give the first terms of the low temperature expansion of the one-point functions for the Ising model in a magnetic field.