Engineering Local optimality in Quantum Monte Carlo algorithms

TL;DR

This paper develops a locally optimal formulation of quantum Monte Carlo algorithms, specifically the worm and directed loop algorithms, to improve their efficiency in simulating spin and bosonic models.

Contribution

It introduces a new locally optimal approach for quantum Monte Carlo algorithms, enhancing their performance by leveraging intrinsic degrees of freedom.

Findings

Improved efficiency in simulating Bose-Hubbard and spin models.

Demonstrated advantages of the locally optimal formulation.

Numerical validation of the new algorithms.

Abstract

Quantum Monte Carlo algorithms based on a world-line representation such as the worm algorithm and the directed loop algorithm are among the most powerful numerical techniques for the simulation of non-frustrated spin models and of bosonic models. Both algorithms work in the grand-canonical ensemble and have a non-zero winding number. However, they retain a lot of intrinsic degrees of freedom which can be used to optimize the algorithm. We let us guide by the rigorous statements on the globally optimal form of Markov chain Monte Carlo simulations in order to devise a locally optimal formulation of the worm algorithm while incorporating ideas from the directed loop algorithm. We provide numerical examples for the soft-core Bose-Hubbard model and various spin-S models.