The MBL can exist in a variety of systems (1D). 

Fermions
* Isolated weakly interacting (repulsive) electrons can have a finite temperature transition into an insulating state (conductivity exactly zero belows certain temperature, determined by interaction strength) [[baa]]
* Strongly (repulsive) interacting fermions can have MBL state even at very high temperatures [[oh]]
* attractive fermions have a transition between superconductivity and localization [[giam]]

Spins
* Hisenberg model with random onsite fields for strong enough disorder shows localization for high energy states [[ph]][[imbre]]

Bosons
* for repulsive bosons with weak dsiorder superfluidity persists [[giam]]
* Tonks–Girardeau in random potential is localized, with no superfluidity down to zero T. [[Seir]][[Stolz]]

Random Circuit models
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