122 research outputs found
A review of Monte Carlo simulations for the Bose-Hubbard model with diagonal disorder
We review the physics of the Bose-Hubbard model with disorder in the chemical
potential focusing on recently published analytical arguments in combination
with quantum Monte Carlo simulations. Apart from the superfluid and Mott
insulator phases that can occur in this system without disorder, disorder
allows for an additional phase, called the Bose glass phase. The topology of
the phase diagram is subject to strong theorems proving that the Bose Glass
phase must intervene between the superfluid and the Mott insulator and implying
a Griffiths transition between the Mott insulator and the Bose glass. The full
phase diagrams in 3d and 2d are discussed, and we zoom in on the insensitivity
of the transition line between the superfluid and the Bose glass in the close
vicinity of the tip of the Mott insulator lobe. We briefly comment on the
established and remaining questions in the 1d case, and give a short overview
of numerical work on related models.Comment: 30 pages, 8 figure
Recent developments in Quantum Monte-Carlo simulations with applications for cold gases
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.Comment: 68 pages, 22 figures, review article; replaced with published versio
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