Y-Systems for Generalised Gibbs Ensembles in Integrable Quantum Field Theory

TL;DR

This paper extends the thermodynamic Bethe ansatz framework to derive Y-systems for generalized Gibbs ensembles in integrable quantum field theories, revealing shared Y-systems across many ensembles.

Contribution

It introduces a derivation of Y-systems for generalized Gibbs ensembles, broadening the understanding of thermodynamic structures in integrable quantum field theories.

Findings

Y-systems can be derived for generalized Gibbs ensembles

Many integrable quantum field theories share the same Y-system across different ensembles

Y-systems retain key properties like periodicity and fixed points in the generalized context

Abstract

The thermodynamic Bethe ansatz approach to the study of integrable quantum field theories was introduced in the early 90s. Since then it has been known that the thermodynamic Bethe ansatz equations can be recast in the form of $Y$-systems. These $Y$-systems have a number of interesting properties, notably in the high-temperature limit their solutions are constants from which the central charge of the ultraviolet fixed point can be obtained and they are typically periodic functions, with period proportional to the dimension of the perturbing field. In this letter we discuss the derivation of $Y$-systems when the standard thermodynamic Bethe ansatz equations are replaced by generalised versions, describing generalised Gibbs ensembles. We shown that for many integrable quantum field theories, there is a large class of distinct generalised Gibbs ensembles which share the same $Y$-system.