A quantum Monte Carlo algorithm for Bose-Hubbard models on arbitrary graphs

TL;DR

This paper introduces a versatile quantum Monte Carlo algorithm for simulating Bose-Hubbard models on any graph, simplifying adaptation to various geometries without custom updates.

Contribution

The authors develop a general quantum Monte Carlo method that automatically adapts to arbitrary graph structures using cycle basis generation.

Findings

Successfully simulated Bose-Hubbard models on 2D lattices and random graphs.

Demonstrated the method's efficiency and automation in handling different geometries.

Validated the approach with numerical results across various graph types.

Abstract

We propose a quantum Monte Carlo algorithm capable of simulating the Bose-Hubbard model on arbitrary graphs, obviating the need for devising lattice-specific updates for different input graphs. We show that with our method, which is based on the recently introduced Permutation Matrix Representation Quantum Monte Carlo [Gupta, Albash and Hen, J. Stat. Mech. (2020) 073105], the problem of adapting the simulation to a given geometry amounts to generating a cycle basis for the graph on which the model is defined, a procedure that can be carried out efficiently and and in an automated manner. To showcase the versatility of our approach, we provide simulation results for Bose-Hubbard models defined on two-dimensional lattices as well as on a number of random graphs.