Auxiliary-Field Monte Carlo for lattice bosons: tackling strong interactions and frustration

TL;DR

The paper presents a new bosonic auxiliary-field Monte Carlo method that efficiently computes thermal properties of large lattice-boson systems, effectively handling strong interactions and frustration without sign problems.

Contribution

It introduces a systematically improvable semiclassical cluster-based Monte Carlo approach applicable to any bosonic model, overcoming sign problems and enabling accurate predictions.

Findings

Reproduces exact superfluid transition results for hardcore bosons on square lattices.

Provides quantitative predictions for superfluid and chiral transitions on frustrated triangular lattices.

Eliminates sign problems through a cluster-separable state approximation.

Abstract

We introduce a new numerical technique -- bosonic auxiliary-field Monte Carlo (bAFMC) -- which allows to calculate the thermal properties of large lattice-boson systems within a systematically improvable semiclassical approach, and which is virtually applicable to any bosonic model. Our method amounts to a decomposition of the lattice into clusters, and to an Ansatz for the density matrix of the system in the form of a cluster-separable state -- with non-entangled, yet classically correlated clusters. This approximation eliminates any sign problem, and can be systematically improved upon by using clusters of growing size. Extrapolation in the cluster size allows to reproduce numerically exact results for the superfluid transition of hardcore bosons on the square lattice, and to provide a solid quantitative prediction for the superfluid and chiral transition of hardcore bosons on the frustrated triangular lattice.