Topological Phase Transitions and Holonomies in the Dimer Model

TL;DR

This paper explores topological phase transitions and holonomy effects in the classical dimer model on a toroidal lattice, revealing connections to Dirac fermions and topological degeneracies.

Contribution

It demonstrates the emergence of holonomy phases and topological phase transitions in the dimer model, linking lattice properties to continuum Dirac fermion theories.

Findings

Holonomy phases appear in the thermodynamic limit.

Finite size corrections relate to a massless Dirac Fermion with flat connection.

The phase transition is topological, with the torus degenerating at criticality.

Abstract

We demonstrate that the classical dimer model defined on a toroidal hexagonal lattice acquires holonomy phases in the thermodynamic limit. When all activities are equal the lattice sizes must be considered mod 6 in which case the finite size corrections to the bulk partition function correspond to a massless Dirac Fermion in the presence of a flat connection with nontrivial holonomy. For general bond activities we find that the phase transition in this model is a topological one, where the torus degenerates and its modular parameter becomes real at the critical temperature. We argue that these features are generic to bipartite dimer models and we present a more general lattice whose continuum partition function is that of a massive Dirac Fermion.