Many-body localization for disordered Bosons

Abstract

Concrete models of interacting quantum systems for which expected manifestations of the manybody localized phase can be rigorously verified are in short supply. Recent work by Seiringer and Warzel (2016 New J. Phys. 18 035002) succeeds in deriving such properties for a disordered Tonks-Girardeau gas. This provides a first example of a Boson gas in the strong Bose glass phase, characterized by the absence of Bose-Einstein condensation as well as the absence of superfluidity at zero temperature. The derivation exploits new mathematical tools to overcome problems arising from the non-locality of Fermionic wave functions associated with the states of a Tonks-Girardeau gas.

Asymptotic localization in the Bose-Hubbard model

“…given by (42), then we see that r(ad −1 d (Id −R)f ) = r(f ). From this and (46 -48) we readily deduce (53).…”

“…From (58) we see that the leading contribution to the generator is µû (1) . Lets write the reduced hoppingv = ρv (ρ) as a sum over nearest neighbour hoppings, it then follows from (42) and (45) that…”

Decay of Complex-Time Determinantal and Pfaffian Correlation Functionals in Lattices

“…This last paper has attracted much attention and it has already been cited many times in one and a half year. See, e.g., [5][6][7][8][9][10][11][12][13].…”

Non-ergodic extended states in the SYK model

“…Introduction:-In recent years, classifications of many body quantum systems as either 'ergodic', or 'many body localized' (MBL) have become mainstream. This reflects the discovery of a growing number of systems supporting MBL phases [1][2][3][4][5][6][7][8][9][10][11][12] and naturally extends the distinction between single particle ergodic and Anderson localized systems to many body quantum disorder. However, recently, we are seeing mounting evidence [13][14][15][16][17][18][19][20][21] that the above dichotomy may be too coarse to capture the complexity of chaotic many body systems.…”