Recent developments in Quantum Monte-Carlo simulations with applications for cold gases

TL;DR

This review summarizes recent advances in Quantum Monte Carlo methods applied to ultra cold gases, highlighting developments in simulating bosonic and fermionic systems, and their experimental validations.

Contribution

It provides a comprehensive overview of new Monte Carlo techniques and their applications to various cold gas systems, including long-range interactions and disordered systems.

Findings

Path integral Monte Carlo with worm updates agrees with experiments.

Sign-free determinantal methods at half filling for fermions.

Advances in diagrammatic Monte Carlo and diffusion Monte Carlo.

Abstract

This is a review of recent developments in Monte Carlo methods in the field of ultra cold gases. For bosonic atoms in an optical lattice we discuss path integral Monte Carlo simulations with worm updates and show the excellent agreement with cold atom experiments. We also review recent progress in simulating bosonic systems with long-range interactions, disordered bosons, mixtures of bosons, and spinful bosonic systems. For repulsive fermionic systems determinantal methods at half filling are sign free, but in general no sign-free method exists. We review the developments in diagrammatic Monte Carlo for the Fermi polaron problem and the Hubbard model, and show the connection with dynamical mean-field theory. We end the review with diffusion Monte Carlo for the Stoner problem in cold gases.