Inverted many-body mobility edge in a central qudit problem

TL;DR

This paper uncovers an inverted many-body mobility edge in a disordered central qudit model, revealing high energy localization and low energy delocalization, with implications for cavity QED and central spin systems.

Contribution

It demonstrates the existence of an inverted mobility edge in a central qudit model and analyzes the critical energy scaling and reentrant MBL phases.

Findings

High energy states are localized, low energy states are delocalized.

Critical energy scales as E_c ∝ L^{1/2}.

Evidence of reentrant MBL phase at low energies.

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.