Current operators in integrable models: A review

TL;DR

This review discusses current operators in one-dimensional integrable models, highlighting their role in Generalized Hydrodynamics, presenting exact formulas, new results, and implications for dynamical correlations.

Contribution

It provides a comprehensive overview of current operators, including new calculations for Heisenberg chains and simplified formulas, advancing understanding in integrable models.

Findings

Exact formulas for mean currents in finite and infinite volume

New computations of currents in Heisenberg spin chains

Simplified thermodynamic limit formulas

Abstract

We consider the current operators of one dimensional integrable models. These operators describe the flow of the conserved charges of the models, and they play a central role in Generalized Hydrodynamics. We present the key statements about the mean currents in finite volume and in the thermodynamic limit, and we review the various proofs of the exact formulas. We also present a few new results in this review. New contributions include a computation of the currents of the Heisenberg spin chains using the string hypothesis, and simplified formulas in the thermodynamic limit. We also discuss implications of our results for the asymptotic behaviour of dynamical correlation functions.