What is the difference between localization in a many-body localization system and localization in a Mott insulator? Is the difference that many-body localization is driven by disorder while Mott insulating is driven by interaction?

Another more general question: Is many-body localization inherently quantum? Several papers describe many-body localization as a quantum phase transition, what role does quantum fluctuation play in many-body localization?

  • $\begingroup$ Do you mean Anderson localization? That's the one you get due to disorder. $\endgroup$ – Lagerbaer Feb 29 '16 at 1:06
  • $\begingroup$ @Lagerbaer Many-body localisation is the generalisation of Anderson localisation (which is a property of the disordered single-particle problem) to interacting many-body systems. $\endgroup$ – Mark Mitchison Feb 29 '16 at 3:03
  • $\begingroup$ @SlipStream There is very little relation between the two concepts, really, except that transport coefficients would vanish in both cases. For example, many-body localised systems can never reach thermal equilibrium, whereas a Mott insulator is a system in thermal equilibrium (or close to it). $\endgroup$ – Mark Mitchison Feb 29 '16 at 3:05
  • $\begingroup$ @MarkMitchison Thanks for the comment. Is it then reasonable to say that disorder is what gives many-body localization its special properties? $\endgroup$ – SlipStream Feb 29 '16 at 4:00

1) I don't see the relation to the Mott insulator. Many-body localization is the absence of thermalization in certain (non-integrable) many-body systems. The Mott insulator is a perfectly good equilibrium phase.

2) There is a relation to Anderson localization. Anderson localization is (essentially) about the motion of a single particle in a random potential. The typical example of many-body localization is a many-body system in a random potential.

3) There is no notion of temperature in the MB localized phase, so the control parameter is something like the disorder strength. Also, there is no thermodynamic entropy, only entanglement entropy. So in that sense, it looks like a quantum phase transition. I'm not sure if anybody knows whether there is universality near the transition.

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