Quantum group symmetries and completeness for A_{2n}^(2) open spin chains

TL;DR

This paper investigates the symmetries of A_{2n}^(2) open quantum spin chains, revealing their quantum group symmetries and providing formulas for Bethe state labels, confirming the Bethe ansatz's spectral predictions.

Contribution

It establishes the quantum group symmetries U_q(B_n) and U_q(C_n) for specific boundary conditions and derives a formula for Bethe state labels, verifying spectral degeneracies.

Findings

Quantum group symmetries are U_q(B_n) and U_q(C_n).

Derived a formula for Bethe state Dynkin labels.

Confirmed spectral degeneracies match Bethe ansatz predictions.

Abstract

We argue that the Hamiltonians for A_{2n}^(2) open quantum spin chains corresponding to two choices of integrable boundary conditions have the symmetries U_q(B_n) and U_q(C_n), respectively. We find a formula for the Dynkin labels of the Bethe states (which determine the degeneracies of the corresponding eigenvalues) in terms of the numbers of Bethe roots of each type. With the help of this formula, we verify numerically (for a generic value of the anisotropy parameter) that the degeneracies and multiplicities of the spectra implied by the quantum group symmetries are completely described by the Bethe ansatz.