Dynamics of the quantum dimer model on the triangular lattice: Soft modes and local resonating valence-bond correlations

TL;DR

This study investigates the dynamical properties of the quantum dimer model on a triangular lattice, revealing soft modes and phase transition characteristics through advanced Monte Carlo simulations.

Contribution

It provides the first detailed analysis of dynamical dimer correlations and the nature of the ordered phase in this model, highlighting unexpected features in the Bragg peaks.

Findings

Soft modes emerge as dimer repulsion decreases.

A second-order phase transition occurs into an ordered phase.

Only two of three high-symmetry points show significant Bragg peaks.

Abstract

We report on an exhaustive investigation of the dynamical dimer-dimer correlations in imaginary time for the quantum dimer model on the triangular lattice using the Green's function Monte Carlo method. We show in particular that soft modes develop upon reducing the dimer-dimer repulsion, indicating the presence of a second-order phase transition into an ordered phase with broken translational symmetry. We further investigate the nature of this ordered phase, for which a 12-site unit cell has been previously proposed, with the surprising result that significant Bragg peaks are only present at two of the three high-symmetry points consistent with this unit cell. We attribute the absence of a detectable peak to its small magnitude due to the nearly uniform internal structure of the 12-site crystal cell.