$T\bar{T}$ deformations and integrable spin chains

TL;DR

This paper extends $Tar{T}$ deformations to integrable spin chains by defining a deformation via the S matrix in Bethe equations, showing it preserves integrability and is constructed from lattice currents.

Contribution

It introduces a new class of current-current deformations for integrable spin chains, generalizing $Tar{T}$ deformations from quantum field theory to lattice models.

Findings

Deformation modifies the S matrix in Bethe equations.

Deformation operator is composite, built from two lattice currents.

The deformation preserves the integrable structure of the model.

Abstract

We consider current-current deformations that generalise $T\bar{T}$ ones, and show that they may be also introduced for integrable spin chains. In analogy with the integrable QFT setup, we define the deformation as a modification of the S matrix in the Bethe equations. Using results by Bargheer, Beisert and Loebbert we show that the deforming operator is composite and constructed out of two currents on the lattice; its expectation value factorises like for $T\bar{T}$. Such a deformation may be considered for any combination of charges that preserve the model's integrable structure.