SU(2)-invariant continuum theory for an unconventional phase transition in a three-dimensional classical dimer model

TL;DR

This paper develops an SU(2)-invariant continuum theory for an unconventional phase transition in a 3D classical dimer model, linking it to a 2D quantum superfluid-Mott insulator transition via a lattice mapping.

Contribution

It introduces a novel continuum field theory for the dimer model transition, connecting classical and quantum models through a new SU(2)-invariant framework.

Findings

Derivation of a continuum theory for the dimer transition.

Mapping of the classical problem to a quantum boson model.

Identification of the transition as a superfluid-Mott insulator transition.

Abstract

We derive a continuum theory for the phase transition in a classical dimer model on the cubic lattice, observed in recent Monte Carlo simulations. Our derivation relies on the mapping from a three-dimensional classical problem to a two-dimensional quantum problem, by which the dimer model is related to a model of hard-core bosons on the kagome lattice. The dimer-ordering transition becomes a superfluid-Mott insulator quantum phase transition at fractional filling, described by an SU(2)-invariant continuum theory.