Renormalization, duality, and phase transitions in two- and three-dimensional quantum dimer models

TL;DR

This paper develops an extended lattice gauge theory for quantum dimer models in 2D and 3D, analyzing their phase structures, dualities, and phase transitions, including KT and first-order transitions at various temperatures.

Contribution

It introduces a novel extended gauge theory framework for quantum dimer models and explores their phase diagrams and dualities in two and three dimensions.

Findings

Identifies a critical point at the RK point related to $Z_N$ models in 2D.

Discovers two phase transitions in 2D, including a KT transition at finite temperature.

Finds a first-order phase transition in 3D at zero temperature.

Abstract

We derive an extended lattice gauge theory type action for quantum dimer models and relate it to the height representations of these systems. We examine the system in two and three dimensions and analyze the phase structure in terms of effective theories and duality arguments. For the two-dimensional case we derive the effective potential both at zero and finite temperature. The zero-temperature theory at the Rokhsar-Kivelson (RK) point has a critical point related to the self-dual point of a class of $Z_N$ models in the $N\to\infty$ limit. Two phase transitions featuring a fixed line are shown to appear in the phase diagram, one at zero temperature and at the RK point and another one at finite temperature above the RK point. The latter will be shown to correspond to a Kosterlitz-Thouless (KT) phase transition, while the former will be governed by a KT-like universality class, i.e., sharing many features with a KT transition but actually corresponding to a different universality class. On the other hand, we show that at the RK point no phase transition happens at finite temperature. For the three-dimensional case we derive the corresponding dual gauge theory model at the RK point. We show in this case that at zero temperature a first-order phase transition occurs, while at finite temperatures both first- and second-order phase transitions are possible, depending on the relative values of the couplings involved.