Algebraic Bethe ansatz for the totally asymmetric simple exclusion process with boundaries

TL;DR

This paper applies the algebraic Bethe ansatz to solve the eigenproblem of the TASEP with boundary reservoirs, extending the method to non-diagonal boundary conditions and providing a proof of its validity.

Contribution

It introduces a modified algebraic Bethe ansatz approach for TASEP with boundaries and proves its correctness for this model.

Findings

Eigenvalues and eigenvectors computed explicitly

Method extended to non-diagonal boundary conditions

Provides proof of the modified algebraic Bethe ansatz validity

Abstract

We study the one-dimensional totally asymmetric simple exclusion process in contact with two reservoirs including also a fugacity at one boundary. The eigenvectors and the eigenvalues of the corresponding Markov matrix are computed using the modified algebraic Bethe ansatz, method introduced recently to study the spin chain with non-diagonal boundaries. We provide in this case a proof of this method.