Generalized Gibbs Ensemble and string-charge relations in nested Bethe Ansatz

TL;DR

This paper extends the understanding of the Generalized Gibbs Ensemble (GGE) to nested Bethe Ansatz models with $SU(N)$ symmetry, identifying a complete set of quasi-local charges that determine the system's steady states.

Contribution

It introduces a complete set of quasi-local charges for $SU(N)$ nested Bethe Ansatz models derived from transfer matrix fusion, clarifying their role in GGE.

Findings

Complete set of charges obtained from fusion hierarchy.

Charges are quasi-local in certain rapidity regimes.

Charges fix the rapidity distributions for all nesting levels.

Abstract

The non-equilibrium steady states of integrable models are believed to be described by the Generalized Gibbs Ensemble (GGE), which involves all local and quasi-local conserved charges of the model. In this work we investigate integrable lattice models solvable by the nested Bethe Ansatz, with group symmetry $SU(N)$, $N\ge 3$. In these models the Bethe Ansatz involves various types of Bethe rapidities corresponding to the "nesting" procedure, describing the internal degrees of freedom for the excitations. We show that a complete set of charges for the GGE can be obtained from the known fusion hierarchy of transfer matrices. The resulting charges are quasi-local in a certain regime in rapidity space, and they completely fix the rapidity distributions of each string type from each nesting level.