The integrable quantum group invariant A_{2n-1}^(2) and D_{n+1}^(2) open spin chains

TL;DR

This paper identifies new classes of integrable open spin chains with specific quantum group symmetries, analyzes their spectral degeneracies, and proposes Bethe ansatz solutions with numerical validation.

Contribution

It introduces families of A_{2n-1}^(2) and D_{n+1}^(2) integrable open spin chains with quantum group symmetries and provides Bethe ansatz solutions for some models.

Findings

Identified A_{2n-1}^(2) and D_{n+1}^(2) integrable open spin chains with specific symmetries.

Proposed Bethe ansatz solutions and verified their completeness numerically.

Derived formulas linking Bethe roots to spectral degeneracies.

Abstract

A family of A_{2n}^(2) integrable open spin chains with U_q(C_n) symmetry was recently identified in arXiv:1702.01482. We identify here in a similar way a family of A_{2n-1}^(2) integrable open spin chains with U_q(D_n) symmetry, and two families of D_{n+1}^(2) integrable open spin chains with U_q(B_n) symmetry. We discuss the consequences of these symmetries for the degeneracies and multiplicities of the spectrum. We propose Bethe ansatz solutions for two of these models, whose completeness we check numerically for small values of n and chain length N. We find formulas for the Dynkin labels in terms of the numbers of Bethe roots of each type, which are useful for determining the corresponding degeneracies. In an appendix, we briefly consider D_{n+1}^(2) chains with other integrable boundary conditions, which do not have quantum group symmetry.