The Space of Integrable Systems from Generalised $T\bar{T}$-Deformations

TL;DR

This paper extends the generalised $T\bar{T}$-deformation to include all extensive charges, leading to new deformations of S-matrices and revealing that the thermodynamics of these models are governed by thermodynamic Bethe-Ansatz equations and generalized hydrodynamics.

Contribution

It introduces a comprehensive extension of the $T\bar{T}$-deformation that encompasses all extensive charges, connecting it to thermodynamic Bethe-Ansatz and hydrodynamics without relying on integrability assumptions.

Findings

Deformations of S-matrices beyond CDD factors with arbitrary momentum dependence.

Derivation of flow equations for free energy and fluxes from statistical mechanics.

Thermodynamics described by integral equations of the thermodynamic Bethe-Ansatz and expected current forms.

Abstract

We introduce an extension of the generalised $T\bar{T}$-deformation described by Smirnov-Zamolodchikov, to include the complete set of extensive charges. We show that this gives deformations of S-matrices beyond CDD factors, generating arbitrary functional dependence on momenta. We further derive from basic principles of statistical mechanics the flow equations for the free energy and all free energy fluxes. From this follows, without invoking the microscopic Bethe ansatz or other methods from integrability, that the thermodynamics of the deformed models are described by the integral equations of the thermodynamic Bethe-Ansatz, and that the exact average currents take the form expected from generalised hydrodynamics, both in the classical and quantum realms.