Open two-species exclusion processes with integrable boundaries

TL;DR

This paper classifies all integrable boundary conditions for a two-species asymmetric exclusion process, showing how their stationary states can be expressed via matrix product states and illustrating with a detailed example.

Contribution

It provides a complete classification of integrable boundary conditions for the two-species ASEP and constructs explicit matrix product solutions for these models.

Findings

Certain boundary conditions produce non-zero particle currents.

Stationary states can be expressed using matrix product forms.

Explicit example with 9 generators demonstrates the approach.

Abstract

We give a complete classification of integrable Markovian boundary conditions for the asymmetric simple exclusion process with two species (or classes) of particles. Some of these boundary conditions lead to non-vanishing particle currents for each species. We explain how the stationary state of all these models can be expressed in a matrix product form, starting from two key components, the Zamolodchikov-Faddeev and Ghoshal-Zamolodchikov relations. This statement is illustrated by studying in detail a specific example, for which the matrix Ansatz (involving 9 generators) is explicitly constructed and physical observables (such as currents, densities) calculated.