Continuous-time Diffusion Monte Carlo and the Quantum Dimer Model

TL;DR

This paper introduces a continuous-time Diffusion Monte Carlo method for lattice models, effectively studying quantum dimer models and phase transitions, including monomer confinement and deconfinement.

Contribution

It presents a novel continuous-time DMC approach for lattice models that does not rely on trial wavefunctions, enabling detailed phase analysis near Rokhsar-Kivelson points.

Findings

Confirmed deconfined monomers on triangular lattice.

Identified phase transition from confined to deconfined monomers on square lattice.

Calculated potential energy of test monomers at zero temperature.

Abstract

A continuous-time formulation of the Diffusion Monte Carlo method for lattice models is presented. In its simplest version, without the explicit use of trial wavefunctions for importance sampling, the method is an excellent tool for investigating quantum lattice models in parameter regions close to generalized Rokhsar-Kivelson points. This is illustrated by showing results for the quantum dimer model on both triangular and square lattices. The potential energy of two test monomers as a function of their separation is computed at zero temperature. The existence of deconfined monomers in the triangular lattice is confirmed. The method allows also the study of dynamic monomers. A finite fraction of dynamic monomers is found to destroy the confined phase on the square lattice when the hopping parameter increases beyond a finite critical value. The phase boundary between the monomer confined and deconfined phases is obtained.