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


  • 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) [1]
  • Strongly (repulsive) interacting fermions can have MBL state even at very high temperatures [2]
  • attractive fermions have a transition between superconductivity and localization [3]


  • Hisenberg model with random onsite fields for strong enough disorder shows localization for high energy states [4][5]


  • for repulsive bosons with weak dsiorder superfluidity persists [3]
  • Tonks–Girardeau in random potential is localized, with no superfluidity down to zero T. [6]

Random Circuit models


  1. Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states Author links open overlay panelD.M.Basko, I.L.Aleiner, B.L.Altshuler, Annals of Physics Volume 321, Issue 5, May 2006, Pages 1126-1205
  2. Localization of interacting fermions at high temperature Vadim Oganesyan and David A. Huse Phys. Rev. B 75, 155111 – Published 23 April 2007
  3. Giamarchi T and Schulz H J 1988 Anderson localization and interactions in one-dimensional metals Phys. Rev. B 37 325–40
  4. Many-body localization phase transition Arijeet Pal and David A. Huse Phys. Rev. B 82, 174411 – Published 9 November 2010
  5. Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain John Z. Imbrie Phys. Rev. Lett. 117, 027201 – Published 5 July 2016
  6. Decay of correlations and absence of superfluidity in the disordered Tonks–Girardeau gas Robert Seiringer1 and Simone Warzel2 Published 29 February 2016 New Journal of Physics, Volume 18, March 2016