Quantum solids, liquids, and gases program:The solution of the dirty-boson problem

by Prof. Nikolay Prokofiev (University of Massachusetts)

Monday 23 Aug 2010, 11:00 → 12:00 Europe/Stockholm

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.