Abstract
The two primary categories for eigenstate phases of matter at a finite temperature are many-body localization (MBL) and the eigenstate thermalization hypothesis (ETH). We show that, in the paradigmatic quantum -spin models of the spin-glass theory, eigenstates violate the ETH yet are not MBL either. A mobility edge, which we locate using the forward-scattering approximation and replica techniques, separates the nonergodic phase at a small transverse field from an ergodic phase at a large transverse field. The nonergodic phase is also bounded from above in temperature, by a transition in configuration-space statistics reminiscent of the clustering transition in the spin-glass theory. We show that the nonergodic eigenstates are organized in clusters which exhibit distinct magnetization patterns, as characterized by an eigenstate variant of the Edwards-Anderson order parameter.
- Received 14 November 2016
DOI:https://doi.org/10.1103/PhysRevLett.118.127201
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