Construction of Modular Branching Functions from Bethe's Equations in the 3-State Potts Chain

TL;DR

This paper derives modular branching functions for the 3-state Potts chain using Bethe's equations, offering a fermionic perspective that complements existing bosonic models and reveals new correlations and connections to Lee-Yang edge field theory.

Contribution

It introduces a fermionic construction of branching functions from Bethe's equations for the 3-state Potts chain, expanding the theoretical understanding of its conformal field theory aspects.

Findings

Fermionic construction of branching functions for the $D_4$ representation.

Observation of oscillations in correlation functions.

New link between the Potts chain and Lee-Yang edge field theory.

Abstract

We use the single particle excitation energies and the completeness rules of the 3-state anti-ferromagnetic Potts chain, which have been obtained from Bethe's equation, to compute the modular invariant partition function. This provides a fermionic construction for the branching functions of the $D_4$ representation of $Z_4$ parafermions which complements the previous bosonic constructions. It is found that there are oscillations in some of the correlations and a new connection with the field theory of the Lee-Yang edge is presented.