Dual Quantum Monte Carlo Algorithm for Hardcore Bosons

TL;DR

This paper introduces a dual quantum Monte Carlo algorithm for hardcore bosons, derived from the bosonic Hubbard model, enabling efficient numerical simulations and measurement of correlation functions.

Contribution

The paper presents a new dual representation and Monte Carlo algorithm for hardcore bosons, simplifying simulations and allowing direct measurement of order parameter correlations.

Findings

Efficient measurement of order parameter correlations in numerical simulations.

Simplified dual partition function suitable for numerical analysis.

Validation through numerical tests in one dimension.

Abstract

We derive the exact dual representation of the bosonic Hubbard model which takes the form of conserved current loops. The hardcore limit, which corresponds to the quantum spin-${1\over 2}$ Heisenberg antiferromagnet, is also obtained. In this limit, the dual partition function takes a particularly simple form which is very amenable to numerical simulations. In addition to the usual quantities that we can measure (energy, density-density correlation function and superfluid density) we can with this new algorithm measure efficiently the order parameter correlation function, $<a_i a_j^{\dagger}>, |i-j|\ge 1$. We demonstrate this with numerical tests in one dimension.