Scattering matrix for a general gl(2) spin chain

TL;DR

This paper analyzes a general class of gl(2) spin chains with regular site representations, reviews their integrability and spectrum, and proposes a particle interpretation with a conjectured scattering matrix.

Contribution

It introduces a unified framework for gl(2) spin chains with arbitrary regular site representations and conjectures the scattering matrix between particles.

Findings

Review of known integrability results

Spectrum characterization of the spin chain

Conjectured scattering matrix between particles

Abstract

We study the general L_0-regular gl(2) spin chain, i.e. a chain where the sites {i,i+L_0,i+2L_0,...} carry the same arbitrary representation (spin) of gl(2). The basic example of such chain is obtained for L_0=2, where we recover the alternating spin chain. Firstly, we review different known results about their integrability and their spectrum. Secondly, we give an interpretation in terms of particles and conjecture the scattering matrix between them.