Current mean values in the XYZ model

TL;DR

This paper derives an exact formula for the mean values of current operators in the XYZ model, an integrable spin chain without U(1) symmetry, facilitating the study of its transport properties via Generalized Hydrodynamics.

Contribution

It provides the first exact expression for current mean values in the XYZ model for any eigenstate, advancing understanding of transport in non-U(1) symmetric integrable systems.

Findings

Exact current mean values derived for the XYZ model.

Result applicable to any eigenstate in finite volume.

Lays groundwork for transport studies using Generalized Hydrodynamics.

Abstract

The XYZ model is an integrable spin chain which has an infinite set of conserved charges, but it lacks a global $U(1)$-symmetry. We consider the current operators, which describe the flow of the conserved quantities in this model. We derive an exact result for the current mean values, valid for any eigenstate in a finite volume with periodic boundary conditions. This result can serve as a basis for studying the transport properties of this model within Generalized Hydrodynamics.