# Exact results for disordered systems/superfluids I: Theorem of inclusions and the weak disorder limit

Nikolai Prokof'ev, University of Massachusetts Amherst

29.04.2016 at 09:00

I will review two exact results concerning the topology of groundstate phase diagrams for disordered systems and how they project on properties of superfluids.

The theorem of inclusions implies that compressible insulating states always intervene between the fully gaped and conducting phases, or, that direct phase transitions between the Mott insulator and superfluid states are forbidden. Moreover, any transition between the fully gaped and gapless state has to be of the Griffiths type, with important implications for how such a transition should be addressed numerically and experimentally in finite-size systems. For weak disorder, one can use general arguments based on the central limit theorem to establish the shape of the superfluid-to-Bose glass phase boundary in the disorder-interaction plane.

A 450, Theresienstr. 37