Integrable hard rod deformation of the Heisenberg spin chains

TL;DR

This paper introduces new integrable spin-1/2 chain models as hard rod deformations of the XXZ Heisenberg chains, revealing spectral degeneracies and solving them exactly using Bethe Ansatz for specific cases.

Contribution

It develops a novel class of integrable models with multiple particle types, including hard rods, and applies a recent formalism to establish their algebraic integrability.

Findings

Exact spectral degeneracies across different deformations and volumes.

Bethe Ansatz solution provided for the case of hard rods of length 2.

Models support multiple particle types with distinct mobility properties.

Abstract

We present new integrable models of interacting spin-1/2 chains, which can be interpreted as hard rod deformations of the XXZ Heisenberg chains. The models support multiple particle types: dynamical hard rods of length $\ell$ and particles with lengths $\ell'<\ell$ that are immobile except for the interaction with the hard rods. We encounter a remarkable phenomenon in these interacting models: exact spectral degeneracies across different deformations and volumes. The algebraic integrability of these systems is also treated using a recently developed formalism for medium range integrable spin chains. We present the detailed Bethe Ansatz solution for the case $\ell=2$.