Integrability Test for Spin Chains

TL;DR

This paper introduces a heuristic test for quantum chain integrability and applies it to various spin models, identifying all integrable models with o(2) symmetry within a specific family.

Contribution

It proposes a simple heuristic integrability test and characterizes all integrable models with o(2) symmetry in a multiparameter spin-1/2 family.

Findings

Test successfully applied to multiple spin models

Identified all integrable models with o(2) symmetry in the family

Provides a new tool for analyzing quantum chain integrability

Abstract

We examine a simple heuristic test of integrability for quantum chains. This test is applied to a variety of systems, including a generic isotropic spin-1 model with nearest-neighbor interactions and a multiparameter family of spin-1/2 models generalizing the XYZ chain, with next-to-nearest neighbor interactions and bond alternation. Within the latter family we determine all the integrable models with an o(2) symmetry.