Spectrum of transfer matrix for $U_q(B_n)$-invariant $A^{(2)}_{2n}$ open spin chain

TL;DR

This paper derives the eigenvalues of the transfer matrix for a specific open quantum spin chain with $U_q(B_n)$ symmetry, verifying their properties and discussing eigenstates, advancing understanding of integrable models with boundaries.

Contribution

It provides an explicit expression for transfer matrix eigenvalues of the $U_q(B_n)$-invariant open $A^{(2)}_{2n}$ spin chain, including analysis of their properties.

Findings

Eigenvalues expressed explicitly for the transfer matrix.

Verification of correct analyticity and asymptotic behavior.

Brief discussion on the structure of eigenstates.

Abstract

We propose an expression for the eigenvalues of the transfer matrix for the $U_q(B_n)$-invariant open quantum spin chain associated with the fundamental representation of $A^{(2)}_{2n}$. By assumption, the Bethe Ansatz equations are ``doubled'' with respect to those of the corresponding closed chain with periodic boundary conditions. We verify that the transfer matrix eigenvalues have the correct analyticity properties and asymptotic behavior. We also briefly discuss the structure of the eigenstates of the transfer matrix.