Phase diagram of the hexagonal lattice quantum dimer model: Order parameters, ground-state energy, and gaps

TL;DR

This paper maps the phase diagram of the hexagonal lattice quantum dimer model using advanced Monte Carlo and variational methods, confirming the gapped nature of the plaquette phase and analyzing order parameters, energies, and gaps.

Contribution

It introduces an efficient quantum Monte Carlo algorithm with improved cluster updates and provides detailed analysis of the phase diagram and ground state properties.

Findings

The plaquette phase is confirmed to be gapped.

The phase diagram includes multiple distinct phases.

The new algorithm improves simulation acceptance rates.

Abstract

The phase diagram of the quantum dimer model on the hexagonal (honeycomb) lattice is computed numerically, extending on earlier work by Moessner, Sondhi, and Chandra. The different ground state phases are studied in detail using several local and global observables. In addition, we analyze imaginary-time correlation functions to determine ground state energies as well as gaps to the first excited states. This leads in particular to a confirmation that the intermediary so-called plaquette phase is gapped -- a point which was previously advocated with general arguments and some data for an order parameter, but required a more direct proof. On the technical side, we describe an efficient world-line quantum Monte Carlo algorithm with improved cluster updates that increase acceptance probabilities by taking account of potential terms of the Hamiltonian during the cluster construction. The Monte Carlo simulations are supplemented with variational computations.