Variational Monte Carlo method for the Baeriswyl wavefunction: application to the one-dimensional bosonic Hubbard model

TL;DR

This paper introduces a variational Monte Carlo approach using the Baeriswyl wavefunction to study the one-dimensional bosonic Hubbard model, accurately reproducing phase diagrams and properties with a novel wavefunction-based method.

Contribution

It presents a new variational Monte Carlo technique employing the Baeriswyl wavefunction for bosonic lattice models, enabling efficient calculation of phase diagrams and correlations.

Findings

Phase diagram matches quantum Monte Carlo results

Method accurately computes correlation functions

Applicable to one-dimensional bosonic systems

Abstract

A variational Monte Carlo method for bosonic lattice models is introduced. The method is based on the Baeriswyl projected wavefunction. The Baeriswyl wavefunction consists of a kinetic energy based projection applied to the wavefunction at infinite interaction, and is related to the shadow wavefunction already used in the study of continuous models of bosons. The wavefunction at infinite interaction, and the projector, are represented in coordinate space, leading to an expression for expectation values which can be evaluated via Monte Carlo sampling. We calculate the phase diagram and other properties of the bosonic Hubbard model. The calculated phase diagram is in excellent agreement with known quantum Monte Carlo results. We also analyze correlation functions.