Exactly Solvable Models of Interacting Spin-s Particles in one-dimension

TL;DR

This paper presents an exact solution for a class of one-dimensional many-body spin-$s$ particle models with U(1) symmetry, using a unified quantum inverse scattering framework and deriving Bethe ansatz equations.

Contribution

It introduces a unified formulation of the quantum inverse scattering method for arbitrary spin-$s$ particles and derives their spectrum and Bethe ansatz equations.

Findings

Derived the spectrum for spin-$s$ models

Established a recurrence relation for eigenstates

Formulated Bethe ansatz equations for the system

Abstract

We consider the exact solution of a many-body problem of spin-$s$ particles interacting through an arbitrary U(1) invariant factorizable $S$-matrix. The solution is based on a unified formulation of the quantum inverse scattering method for an arbitrary $(2s+1)$-dimensional monodromy matrix. The respective eigenstates are shown to be given in terms of $2s$ creation fields by a general new recurrence relation. This allows us to derive the spectrum and the respective Bethe ansatz equations.