Recent developments in quantum Monte Carlo simulations with applications for cold gases

Rep Prog Phys. 2012 Sep;75(9):094501. doi: 10.1088/0034-4885/75/9/094501. Epub 2012 Aug 10.


This is a review of recent developments in Monte Carlo methods in the field of ultracold 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.

Publication types

  • Research Support, U.S. Gov't, Non-P.H.S.
  • Review

MeSH terms

  • Cold Temperature
  • Computer Simulation
  • Gases / chemistry*
  • Models, Chemical*
  • Models, Molecular*
  • Monte Carlo Method*
  • Quantum Theory*


  • Gases