Exact diagonalization of the quantum supersymmetric $SU_q(n|m)$ model

TL;DR

This paper employs the algebraic nested Bethe ansatz to exactly solve the eigenproblem of the supersymmetric $SU_q(n|m)$ model with open boundaries, revealing its invariance and connection to a supersymmetric t-J model.

Contribution

It provides an exact solution for the supersymmetric $SU_q(n|m)$ model with open boundaries and establishes its $SU_q(n|m)$ invariance, linking it to a multicomponent supersymmetric t-J model.

Findings

Eigenvalues and eigenvectors explicitly obtained

Transfer matrix shown to be $SU_q(n|m)$ invariant

Model related to supersymmetric t-J model under certain conditions

Abstract

We use the algebraic nested Bethe ansatz to solve the eigenvalue and eigenvector problem of the supersymmetric $SU_q(n|m)$ model with open boundary conditions. Under an additional condition that model is related to a multicomponent supersymmetric t-J model. We also prove that the transfer matrix with open boundary condition is $SU_q(n|m)$ invariant.