Thermodynamic bootstrap program for integrable QFT's: Form factors and correlation functions at finite energy density

TL;DR

This paper develops a thermodynamic bootstrap approach for integrable quantum field theories, enabling the calculation of form factors and correlation functions at finite energy density, including finite temperature and generalized Gibbs states.

Contribution

It generalizes form factor axioms to finite energy density states and provides a method to compute correlation functions using these new form factors.

Findings

Exact form factors as minimal solutions of generalized axioms

Correlation functions constructed using thermodynamic form factors

Identification of two infrared regimes: exponential decay and gapless behavior

Abstract

We study the form factors of local operators of integrable QFT's between states with finite energy density. These states arise, for example, at finite temperature, or from a generalized Gibbs ensemble. We generalize Smirnov's form factor axioms, formulating them for a set of particle/hole excitations on top of the thermodynamic background, instead of the vacuum. We show that exact form factors can be found as minimal solutions of these new axioms. The thermodynamic form factors can be used to construct correlation functions on thermodynamic states. The expression found for the two-point function is similar to the conjectured LeClair-Mussardo formula, but using the new form factors dressed by the thermodynamic background, and with all singularities properly regularized. We study the different infrared asymptotics of the thermal two-point function, and show there generally exist two different regimes, manifesting massive exponential decay, or effectively gapless behavior at long distances, respectively. As an example, we compute the few-excitations form factors of vertex operators for the sinh-Gordon model.