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Rare thermal bubbles at the many-body localization transition from the Fock space point of view | | Giuseppe De Tomasi
; Ivan M. Khaymovich
; Frank Pollmann
; Simone Warzel
; | | Date: |
5 Nov 2020 | | Abstract: | In this work we study the many-body localization (MBL) transition and relate
it to the eigenstate structure in the Fock space. Besides the standard
entanglement and multifractal probes, we introduce the radial probability
distribution of eigenstate coefficients with respect to the Hamming distance in
the Fock space from the wave function maximum and relate the cumulants of this
distribution to the properties of the quasi-local integrals of motion in the
MBL phase. We demonstrate non-self-averaging property of the many-body fractal
dimension $D_q$ and directly relate it to the jump of $D_q$ as well as of the
localization length of the integrals of motion at the MBL transition. We
provide an example of the continuous many-body transition confirming the above
relation via the self-averaging of $D_q$ in the whole range of parameters.
Introducing a simple toy-model, which hosts ergodic thermal bubbles, we give
analytical evidences both in standard probes and in terms of newly introduced
radial probability distribution that the MBL transition in the Fock space is
consistent with the avalanche mechanism for delocalization, i.e., the
Kosterlitz-Thouless scenario. Thus, we show that the MBL transition can been
seen as a transition between ergodic states to non-ergodic extended states and
put the upper bound for the disorder scaling for the genuine Anderson
localization transition with respect to the non-interacting case. | | Source: | arXiv, 2011.03048 | | Services: | Forum | Review | PDF | Favorites | |
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