A new equivalence between fused RSOS and loop models

TL;DR

This paper establishes a new equivalence between fused RSOS models and loop models by analyzing topological string net configurations and their amplitudes, revealing connections with known models like the hard hexagon model.

Contribution

It introduces a novel equivalence between fused RSOS and loop models through topological and algebraic analysis of string net amplitudes.

Findings

Doubled Fibonacci theory yields loop models from string net amplitudes.

The hard hexagon model is shown to be equivalent to an anisotropic loop model.

Multiple other equivalences between models are suggested.

Abstract

We consider the topological theories of cond-mat/0404617 and cond-mat/0610583 and study ground state amplitudes of string net configurations which consist of large chunks $G$ of (trivalent) regular lattice. We evaluate these amplitudes in two different ways: first we use the Turaev-Viro prescription to write the amplitude as a sum over labelings of the faces of $G$, and second we use the local rules that constrain the amplitude (the $F$-matrix) to resolve subgraphs in creative ways. In the case of the Doubled Fibonacci theory this second way allows us to produce loop models. In particular, we show that the hard hexagon model is equivalent to an anisotropic loop model. Many other interesting equivalences can presumably be obtained.