Exact solution of the $SU_{q}(n)$ invariant quantum spin chains

TL;DR

This paper extends the Nested Bethe Ansatz to open boundary conditions, providing exact solutions for the eigenvectors, eigenvalues, and thermodynamic properties of $SU_q(n)$ invariant quantum spin chains with fixed boundaries.

Contribution

It generalizes the Nested Bethe Ansatz to open boundaries and derives exact solutions for the $A_{n-1}$ vertex model and $SU_q(n)$ Hamiltonian.

Findings

Exact eigenvectors and eigenvalues for open boundary conditions

Thermodynamic limit solutions for free energy and ground state energy

Boundary contributions included in the energy calculations

Abstract

The Nested Bethe Ansatz is generalized to open boundary conditions. This is used to find the exact eigenvectors and eigenvalues of the $A_{n-1}$ vertex model with fixed open boundary conditions and the corresponding $SU_{q}(n)$ invariant hamiltonian. The Bethe Ansatz equations obtained are solved in the thermodynamic limit giving the vertex model free energy and the hamiltonian ground state energy including the corresponding boundary contributions.