Zero-Temperature Properties of the Quantum Dimer Model on the Triangular Lattice

TL;DR

This study investigates the zero-temperature phases of the quantum dimer model on a triangular lattice using advanced numerical methods, revealing topological degeneracy and phase characteristics consistent with previous finite-temperature analyses.

Contribution

It provides a detailed numerical analysis of the quantum dimer model's phases, including topological degeneracy, using large-scale simulations and finite-size scaling.

Findings

Identification of different phases and topological sectors.

Explicit evidence of topological degeneracy near the Rokhsar-Kivelson point.

Confirmation of the phase diagram proposed by previous studies.

Abstract

Using exact diagonalizations and Green's function Monte Carlo simulations, we have studied the zero-temperature properties of the quantum dimer model on the triangular lattice on clusters with up to 588 sites. A detailed comparison of the properties in different topological sectors as a function of the cluster size and for different cluster shapes has allowed us to identify different phases, to show explicitly the presence of topological degeneracy in a phase close to the Rokhsar-Kivelson point, and to understand finite-size effects inside this phase. The nature of the various phases has been further investigated by calculating dimer-dimer correlation functions. The present results confirm and complement the phase diagram proposed by Moessner and Sondhi on the basis of finite-temperature simulations [Phys. Rev. Lett. {\bf 86}, 1881 (2001)].