Small polaron with generic open boundary conditions revisit: exact solution via the off-diagonal Bethe ansatz

TL;DR

This paper provides an exact solution for the small polaron model with open boundary conditions using the off-diagonal Bethe ansatz, revealing spectral properties of a symmetry-broken fermionic system.

Contribution

It introduces a novel application of the off-diagonal Bethe ansatz to solve the small polaron model with generic boundary terms, including Grassmann-valued fields.

Findings

Exact spectra of the Hamiltonian are derived.

Bethe ansatz equations are explicitly constructed.

The model exhibits U(1) symmetry breaking.

Abstract

The small polaron, an one-dimensional lattice model of interacting spinless fermions, with generic non-diagonal boundary terms is studied by the off-diagonal Bethe ansatz method. The presence of the Grassmann valued non-diagonal boundary fields gives rise to a typical $U(1)$-symmetry-broken fermionic model. The exact spectra of the Hamiltonian and the associated Bethe ansatz equations are derived by constructing an inhomogeneous $T-Q$ relation.