Critical exponents for the FPL^2 model

TL;DR

This paper derives exact analytical expressions for the critical properties of the fully packed double loop model on a square lattice, providing insights into its conformal field theory description and low-lying excitations.

Contribution

It introduces a set of coupled non-linear integral equations derived from Bethe ansatz for the FPL^2 model and computes its central charge and scaling dimensions.

Findings

Exact central charge and scaling dimensions obtained

Scaling dimensions align with the Cartan matrix of sl_4

Numerical analysis confirms theoretical predictions

Abstract

Starting from the Bethe ansatz solution we derive a set of coupled non-linear integral equations for the fully packed double loop model (FPL^2) on the square lattice. As an application we find exact expressions for the central charge and for the scaling dimension corresponding to the simplest charge excitation. We study numerically the low-lying excitations corresponding to more general perturbations of the ground state and discover that the corresponding scaling dimensions are well described by the Cartan matrix of sl_4.