Quantum Group Invariant Integrable n-State Vertex Models with Periodic Boundary Conditions

TL;DR

This paper analyzes an $U_q(sl(n))$ invariant integrable vertex model with periodic boundary conditions at roots of unity, revealing its connection to a Virasoro algebra with a specific central charge through finite size analysis.

Contribution

It introduces a novel analysis of $U_q(sl(n))$ invariant models at roots of unity using algebraic nested Bethe ansatz, linking topological features to conformal field theory.

Findings

Derived the central charge as c=(n-1)[1 - n(n+1)/(r(r-1))]

Connected the model's topology to Virasoro algebra properties

Applied finite size analysis to determine conformal data.

Abstract

An $U_q(sl(n))$ invariant transfer matrix with periodic boundary conditions is analysed by means of the algebraic nested Bethe ansatz for the case of $q$ being a root of unity. The transfer matrix corresponds to a 2-dimensional vertex model on a torus with topological interaction w.r.t. the 3-dimensional interior of the torus. By means of finite size analysis we find the central charge of the corresponding Virasoro algebra as $c=(n-1) \left[1-n(n+1)/(r(r-1))\right] $.