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Localization protects quantum order

David Huse - 2013 Localization protected quantum order

  • ... disordered localized phases via non-thermodynamic transitions in the properties of the many-body eigenstates

... the eigenstate thermalization hypothesis (ETH) [18–20]

The many-body localization phase transition is an eigenstate phase transition from the thermal phase where the exact many-body eigenstates obey the ETH, to the localized phase where the eigenstates violate the ETH

The eigenstates of the disordered versions of these Hamiltonians are localized and can be described in terms of noninteracting localized fermions. Ref. [10] showed that this localization is robust to weak fermion-fermion interactions, and we assume in this paper that this is indeed true

  • .... a ‘spectral transition’ involving a sharp change in the spectral statistics of the many-body Hamiltonian.

our discussion is not about ground states or low-lying excited states, but is about highly-excited eigenstates at energies that would
correspond to nonzero (even infinite) temperature if the system could thermalize at these energies

C. Spectral transition in the ordered phase
In the MBL spin-glass phase, all eigenstates come in parity-related pairs which differ only by their occupation of the single particle edge mode created by

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