Spectral equivalences and symmetry breaking in integrable SU_q(N) spin chains with boundaries

TL;DR

This paper explores spectral equivalences in SU_q(N) spin chains with various boundary conditions, revealing how non-diagonal boundaries relate to diagonal ones and analyzing symmetry breaking effects.

Contribution

It establishes spectral equivalences between chains with diagonal and non-diagonal boundary terms, providing insights into residual symmetries despite symmetry breaking.

Findings

Spectral equivalences connect diagonal and non-diagonal boundary chains.

Residual symmetries are understood through these spectral mappings.

Non-diagonal boundary terms break quantum group symmetry, but equivalences help analyze remaining symmetries.

Abstract

We consider the SU_q (N) invariant spin chain with diagonal and non-diagonal integrable boundary terms. The algebraic study of spin chains with different types of boundary terms is used to motivate a set of spectral equivalences between integrable chains with purely diagonal boundary terms and ones with an arbitrary non-diagonal term at one end. For each choice of diagonal boundary terms there is an isospectral one-boundary problem and vice-versa. The quantum group SU_q (N) symmetry is broken by the presence of a non-diagonal boundary term however one can use the spectral equivalence with the diagonal chain to easily understand the residual symmetries of the system.