Inverted many-body mobility edge in a central qudit problem

• URL: http://arxiv.org/abs/2008.12796v1
• Date: Fri, 28 Aug 2020 18:01:38 GMT
• Title: Inverted many-body mobility edge in a central qudit problem
• Authors: Saeed Rahmanian Koshkaki, Michael H. Kolodrubetz
• Abstract summary: We study energy-dependent localization in the disordered Ising model with transverse and longitudinal fields coupled globally to a $d$-level system. Strikingly, we discover an inverted mobility edge, where high energy states are localized while low energy states are delocalized.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Many interesting experimental systems, such as cavity QED or central spin models, involve global coupling to a single harmonic mode. Out-of-equilibrium, it remains unclear under what conditions localized phases survive such global coupling. We study energy-dependent localization in the disordered Ising model with transverse and longitudinal fields coupled globally to a $d$-level system (qudit). Strikingly, we discover an inverted mobility edge, where high energy states are localized while low energy states are delocalized. Our results are supported by shift-and-invert eigenstate targeting and Krylov time evolution up to $L=13$ and $18$ respectively. We argue for a critical energy of the localization phase transition which scales as $E_c \propto L^{1/2}$, consistent with finite size numerics. We also show evidence for a reentrant MBL phase at even lower energies despite the presence of strong effects of the central mode in this regime. Similar results should occur in the central spin-$S$ problem at large $S$ and in certain models of cavity QED.

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