Analytical Bethe Ansatz for $A^{(2)}_{2n-1}, B^{(1)}_n, C^{(1)}_n, D^{(1)}_n$ quantum-algebra-invariant open spin chains

TL;DR

This paper derives the eigenvalues of transfer matrices for integrable open quantum spin chains associated with specific affine Lie algebras, advancing understanding of their spectral properties and algebraic structures.

Contribution

It provides explicit eigenvalue formulas for transfer matrices of quantum spin chains with affine Lie algebra symmetries, a novel analytical result in integrable models.

Findings

Eigenvalues explicitly determined for the transfer matrices.

Results apply to chains with specific affine Lie algebra symmetries.

Enhances understanding of algebraic structures in integrable quantum spin chains.

Abstract

We determine the eigenvalues of the transfer matrices for integrable open quantum spin chains which are associated with the affine Lie algebras $A^{(2)}_{2n-1}, B^{(1)}_n, C^{(1)}_n, D^{(1)}_n$, and which have the quantum-algebra invariance U_q(C_n), U_q(B_n), U_q(C_n), U_q(D_n)$, respectively.