Description
I will discuss the theorem of inclusions which makes
important rigorous statements about phase transitions in
disordered systems and how it applies to the phase diagram
of the disordered three-dimensional Bose-Hubbard model at
unity filling which has been controversial for many years.
The theorem of inclusions states that transitions between
fully gaped and superfluid phases are forbidden and there
must exist an intermediate gapless insulating phase.
The other result is that all transitions between gapfull and
gapless phases have to be of the Griffiths type when the
vanishing of the gap at the critical point is due to a zero
concentration of rare regions where extreme fluctuations of
disorder mimic a regular gapless system. I will also explain
the vortex phase mechanism governing the shape of the phase
diagram in the vicinity of the diagram tip in d=1,2. A
highly non-trivial overall shape of the phase
diagram in d=3 is revealed with the worm algorithm; it
features a long superfluid finger at strong disorder and
on-site interaction. Moreover, bosonic superfluidity is
extremely robust against disorder in a broad range of
interaction parameters; it persists in random potentials
nearly 50 (!) times larger than the particle half-bandwidth.
Finally, we comment on the feasibility of obtaining this
phase diagram in cold-atom experiments, which work with
trapped systems at finite temperature.
Primary author
Prof.
Nikolay Prokofiev
(University of Massachusetts)
