The exact solution and the finite size behaviour of the $Osp(1|2)$ invariant spin chain

TL;DR

This paper provides an exact solution for the $Osp(1|2)$ spin chain using Bethe ansatz, revealing finite size behavior governed by a conformal field theory with central charge 1.

Contribution

It establishes an exact Bethe ansatz solution for the $Osp(1|2)$ spin chain and explores its finite size properties and sector distinctions.

Findings

Exact Bethe ansatz solution for $Osp(1|2)$ chain

Finite size behavior linked to $c=1$ conformal field theory

Identification of phase factors distinguishing sectors

Abstract

We have solved exactly the $Osp(1|2)$ spin chain by the Bethe ansatz approach. Our solution is based on an equivalence between the $Osp(1|2)$ chain and certain special limit of the Izergin-Korepin vertex model. The completeness of the Bethe ansatz equations is discussed for a system with four sites and it is noted the appearance of special string structures. The Bethe ansatz presents an important phase-factor which distinguishes the even and odd sectors of the theory. The finite size properties are governed by a conformal field theory with central charge $c=1$.