Classical to quantum mapping for an unconventional phase transition in a three-dimensional classical dimer model

TL;DR

This paper investigates a unique phase transition in a 3D classical dimer model by mapping it to a 2D quantum boson model, revealing a non-Landau-Ginzburg-Wilson class transition described by a U(1) gauge theory with SU(2) matter fields.

Contribution

It introduces a novel mapping from a classical dimer model to a quantum boson model and characterizes the resulting unconventional phase transition beyond traditional paradigms.

Findings

Identifies a superfluid to Mott insulator transition at fractional filling.

Shows the transition is described by a U(1) gauge theory with SU(2) matter fields.

Demonstrates the transition cannot be captured by Landau-Ginzburg-Wilson theory.

Abstract

We study the transition between a Coulomb phase and a dimer crystal observed in numerical simulations of the three-dimensional classical dimer model, by mapping it to a quantum model of bosons in two dimensions. The quantum phase transition that results, from a superfluid to a Mott insulator at fractional filling, belongs to a class that cannot be described within the Landau-Ginzburg-Wilson paradigm. Using a second mapping, to a dual model of vortices, we show that the long-wavelength physics near the transition is described by a U(1) gauge theory with SU(2) matter fields.