$T\bar T$-deformation and long range spin chains

TL;DR

This paper reveals a deep connection between $T\bar T$-deformations of quantum field theories and long-range deformations of quantum spin chains, showing they share algebraic structures and preserve integrability.

Contribution

It demonstrates that $T\bar T$-deformations and long-range spin chain deformations are formally identical, sharing algebraic origin and integrability properties, opening new research directions.

Findings

Both deformations preserve integrability.

They lead to non-local deformed theories.

A factorisation formula for operator expectation values is proved.

Abstract

We point out that two classes of deformations of integrable models, developed completely independently, have deep connections and share the same algebraic origin. One class includes the $T\bar T$-deformation of 1+1 dimensional integrable quantum field theory and related solvable irrelevant deformations proposed recently. The other class is a specific type of long range integrable deformation of quantum spin chains introduced a decade ago, in the context of $\mathcal{N} = 4$ super-Yang-Mills theory. We show that the detailed structures of the two deformations are formally identical and therefore share many features. Both deformations preserve integrability and lead to non-local deformed theories, resulting in a change of the corresponding factorized S-matrices. We also prove a factorisation formula for the expectation value of the operators which trigger the deformation on the lattice; similar results in quantum field theory play an essential role in the solvability of such deformations. We point out that the long range deformation is a natural counterpart of the $T\bar T$-deformation for integrable spin chains, and argue that this observation leads to interesting new avenues to explore.