##  David Huse - 2013 [Localization protected quantum order](https://boulderschool.yale.edu/sites/default/files/files/Huse,%20et%20al_,%20PRB%20in%20press,%20arXiv%201304_1158.pdf)

-  ... 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

## questions 

- [a relation with Kurchan-Parisi?](https://knowen.org/nodes/28012?path=1-18-60-27709-27862-28012)

- 2007 [Thermalization and its mechanism for generic isolated quantum systems](https://arxiv.org/abs/0708.1324)
Marcos Rigol, Vanja Dunjko, Maxim Olshanii