Spectrum-preserving deformations of integrable spin chains with open boundaries

TL;DR

This paper introduces a family of local deformations called iso-BAE flow that preserve part of the spectrum in integrable quantum spin chains with open boundaries, revealing protected states and spectral degeneracies.

Contribution

It identifies and analyzes the iso-BAE flow, a novel deformation preserving the Bethe Ansatz equations and part of the spectrum in integrable spin chains, including generalizations to various models.

Findings

Part of the spectrum remains invariant under the iso-BAE flow.

Protected states are associated with an emergent symmetry.

Spectral degeneracies depend on chain length parity.

Abstract

We discover a family of local deformations that leave part of the spectrum intact for strongly interacting and exactly solvable quantum many-body systems. Since the deformation preserves the Bethe Ansatz equations (BAE), it is dubbed the iso-BAE flow. Although all theories on the flow share the same BAE, the spectra are different. Part of the spectrum remains intact along the whole flow. Such states are protected by an emergent symmetry. The remaining parts of the spectrum change continuously along the flow and are doubly degenerate for even length spin chains. For odd length chains, the deformed spectrum also comprises doubly degenerate pairs apart from the sector with magnon number $(L+1)/2$, where $L$ is the length of the spin chain. We discuss the iso-BAE flow for the ${\rm XXX}_{1/2}$ model in detail and show that the iso-BAE flows exist for more general models including $q$-deformed XXZ as well as higher spin ${\rm XXX}_{s}$ spin chains.