Eigenvectors of open XXZ and ASEP models for a class of non-diagonal boundary conditions

TL;DR

This paper generalizes the coordinate Bethe ansatz to solve open XXZ and ASEP models with non-diagonal boundaries, expanding the class of solvable models and providing explicit eigenvector representations.

Contribution

It introduces a generalized coordinate Bethe ansatz for non-diagonal boundary conditions, extending known relations and eigenvector representations for integrable models.

Findings

Successfully solves open XXZ and ASEP models with non-diagonal boundaries.

Provides explicit eigenvector expressions as sums over Weyl group cosets.

Extends the parameter relations known in algebraic and functional Bethe ansatz contexts.

Abstract

We present a generalization of the coordinate Bethe ansatz that allows us to solve integrable open XXZ and ASEP models with non-diagonal boundary matrices, provided their parameters obey some relations. These relations extend the ones already known in the literature in the context of algebraic or functional Bethe ansatz. The eigenvectors are represented as sums over cosets of the $BC_n$ Weyl group.