Clustering of non-ergodic eigenstates in quantum spin glasses

C. L. Baldwin; C. R. Laumann; A. Pal; A. Scardicchio

doi:10.1103/physrevlett.118.127201

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arXiv · 1611.02296

Clustering of non-ergodic eigenstates in quantum spin glasses

C. L. Baldwin·C. R. Laumann·A. Pal·A. Scardicchio

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Abstract

The two primary categories for eigenstate phases of matter at finite temperature are many-body localization (MBL) and the eigenstate thermalization hypothesis (ETH). We show that in the paradigmatic quantum $p$-spin models of spin-glass theory, eigenstates violate ETH yet are not MBL either. A mobility edge, which we locate to leading order in $1/p$ using the forward-scattering approximation and replica techniques, separates the non-ergodic phase at small transverse field from an ergodic phase at large transverse field. The non-ergodic phase is also bounded from above in temperature, by a transition in configuration-space statistics reminiscent of the clustering transition in spin-glass theory. We show that the non-ergodic eigenstates are organized in clusters which exhibit distinct magnetization patterns, as characterized by an eigenstate variant of the Edwards-Anderson order parameter.

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C. L. Baldwin, C. R. Laumann, A. Pal, A. Scardicchio. 2017-03-14. Clustering of non-ergodic eigenstates in quantum spin glasses. https://doi.org/10.1103/physrevlett.118.127201

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