Nested algebraic Bethe ansatz for deformed orthogonal and symplectic spin chains

TL;DR

This paper develops a nested algebraic Bethe ansatz method to find exact solutions for deformed orthogonal and symplectic spin chains with quantum group symmetries, extending previous results.

Contribution

It introduces a fusion-based approach to construct higher-dimensional Lax operators and generalizes the Tarasov-Varchenko trace formula for nested Bethe vectors.

Findings

Constructed exact eigenvectors and eigenvalues for $U_q( ext{sp}_{2n})$ and $U_q( ext{so}_{2n})$ spin chains.

Extended the algebraic Bethe ansatz framework to deformed orthogonal and symplectic cases.

Generalized the trace formula for nested Bethe vectors.

Abstract

We construct exact eigenvectors and eigenvalues for $U_q(\mathfrak{sp}_{2n})$- and $U_q(\mathfrak{so}_{2n})$-symmetric closed spin chains by means of a nested algebraic Bethe ansatz method. We use a fusion procedure to construct higher-dimensional Lax operators. Our approach generalises and extends the results obtained by Reshetikhin and De Vega-Karowski. We also present a generalisation of Tarasov-Varchenko trace formula for nested Bethe vectors.