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

摘要

This is a review of recent developments in Monte Carlo methods in the fieldof ultra cold gases. For bosonic atoms in an optical lattice we discuss pathintegral Monte Carlo simulations with worm updates and show the excellentagreement with cold atom experiments. We also review recent progress insimulating bosonic systems with long-range interactions, disordered bosons,mixtures of bosons, and spinful bosonic systems. For repulsive fermionicsystems determinantal methods at half filling are sign free, but in general nosign-free method exists. We review the developments in diagrammatic Monte Carlofor the Fermi polaron problem and the Hubbard model, and show the connectionwith dynamical mean-field theory. We end the review with diffusion Monte Carlofor the Stoner problem in cold gases.