Generalised Hydrodynamics of $\mathrm{T\bar{T}}$-Deformed Integrable Quantum Field Theories

TL;DR

This paper investigates the effects of $ ext{T}ar{ ext{T}}$ deformations on conserved quantities in integrable quantum field theories using Generalised Hydrodynamics, providing exact and approximate results for non-equilibrium states.

Contribution

It extends the understanding of $ ext{T}ar{ ext{T}}$ deformations by deriving exact and approximate formulas for conserved densities and currents in integrable QFTs within the GHD framework.

Findings

Exact expressions for conserved quantities in certain limits.

Generalization of known results to higher spin conserved charges.

Analytic formula for effective inverse temperature in free fermion theory.

Abstract

In this paper we evaluate the averages of conserved densities and currents associated to charges of generic spin in (1+1)-dimensional massive integrable Quantum Field Theories perturbed by the irrelevant $\mathrm{T\bar{T}}$ operator. By making use of the Thermodynamic Bethe Ansatz approach and of the theory of Generalised Hydrodynamics, we study the non-equilibrium steady state averages of conserved densities and currents in a partitioning protocol. We show that in particular limits, averages can be evaluated exactly in terms of quantities known from the unperturbed theory. In the massless limit we recover known results for the energy and momentum currents and generalise those to any higher spin conserved quantities. We extend some of our results to perturbations of the generalised $\mathrm{T\bar{T}}$ type. For the massive free fermion theory, we find an analytic expression for the effective inverse temperature after at $\mathrm{T\bar{T}}$ perturbation in terms of the bare inverse temperature by making use of Lambert's $W$ function.