$T$-$Q$ relations for the integrable two-species asymmetric simple exclusion process with open boundaries

TL;DR

This paper develops $T$-$Q$ relations and Bethe ansatz equations for an integrable two-species ASEP with open boundaries, providing insights into its spectral properties and completeness of solutions.

Contribution

It introduces the nested off-diagonal Bethe ansatz method to derive $T$-$Q$ relations for this model with open boundaries, advancing understanding of its integrability.

Findings

Constructed homogeneous $T$-$Q$ relations for different boundary conditions

Derived Bethe ansatz equations for the two-species ASEP

Numerical checks indicate completeness for some cases

Abstract

We study the integrable two-species asymmetric simple exclusion process (ASEP) for two inequivalent types of open, non particle conserving boundary conditions. Employing the nested off-diagonal Bethe ansatz method, we construct for each case the corresponding homogeneous $T$-$Q$ relations and obtain the Bethe ansatz equations. Numerical checks for small system sizes show completeness for some Bethe ansatz equations, and partial completeness for others.