Continuous-time Diffusion Monte Carlo and the Quantum Dimer Model

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.