Matrix Coordinate Bethe Ansatz: Applications to XXZ and ASEP models

TL;DR

This paper introduces a novel 'matrix coordinate Bethe Ansatz' method that constructs eigenvectors for open ASEP and XXZ models, combining coordinate and matrix Ansatz techniques for integrable systems.

Contribution

It develops a new non-commutative coordinate Bethe Ansatz that unifies previous approaches to solve boundary-driven integrable models.

Findings

Constructed complete eigenvector sets for open ASEP and XXZ models.

Unified coordinate and matrix Ansatz methods for boundary conditions.

Enhanced understanding of spectral properties of these models.

Abstract

We present the construction of the full set of eigenvectors of the open ASEP and XXZ models with special constraints on the boundaries. The method combines both recent constructions of coordinate Bethe Ansatz and the old method of matrix Ansatz specific to the ASEP. This "matrix coordinate Bethe Ansatz" can be viewed as a non-commutative coordinate Bethe Ansatz, the non-commutative part being related to the algebra appearing in