Integrable approach to simple exclusion processes with boundaries. Review and progress

TL;DR

This paper applies integrable systems techniques and the matrix ansatz to analyze boundary-driven exclusion processes and related quantum models, providing new solutions and insights into their structure.

Contribution

It introduces a novel approach combining the matrix ansatz with integrable systems methods to solve boundary-related models in statistical physics.

Findings

Solved a reaction-diffusion model using the combined approach.

Derived an eigenvector for the XXZ spin chain with non-diagonal boundaries.

Provided new insights into the matrix ansatz within the quantum group framework.

Abstract

We study the matrix ansatz in the quantum group framework, applying integrable systems techniques to statistical physics models. We start by reviewing the two approaches, and then show how one can use the former to get new insight on the latter. We illustrate our method by solving a model of reaction-diffusion. An eigenvector for the transfer matrix for the XXZ spin chain with non-diagonal boundary is also obtained using a matrix ansatz.