Loop condensation in the triangular lattice quantum dimer model

TL;DR

This paper investigates how loop condensation leads to topological quantum liquid phases in the triangular lattice quantum dimer model, using Monte Carlo simulations to analyze phase transitions and loop properties.

Contribution

It provides a detailed analysis of loop condensation as a mechanism for topological order in the quantum dimer model on the triangular lattice, including computational characterization.

Findings

Identification of loop condensation as a key mechanism for topological order.

Characterization of dimer-liquid to dimer-crystal phase transitions.

Monte Carlo results on geometric properties of loop distributions.

Abstract

We study the mechanism of loop condensation in the quantum dimer model on the triangular lattice. The triangular lattice quantum dimer model displays a topologically ordered quantum liquid phase in addition to conventionally ordered phases with broken symmetry. In the context of systems with extended loop-like degrees of freedom, the formation of such topological order can be described in terms of loop condensation. Using Monte Carlo calculations with local and directed-loop updates, we compute geometric properties of the transition graph loop distributions of several triangular lattice quantum dimer wavefunctions that display dimer-liquid to dimer-crystal transitions and characterize these in terms of loop condensation.