中心qudit问题中的倒置多体迁移率边
Inverted many-body mobility edge in a central qudit problem
AI总结：
本文研究全局耦合到中心qudit的无序伊辛模型，发现高能局域、低能退局域的倒置迁移率边，并给出临界能量标度E_c ∝ L^{1/2}及更低能量下重入MBL相的证据。
摘要：
许多有趣的实验系统，例如腔QED或中心自旋模型，涉及与单个谐振模式的全局耦合。在非平衡状态下，局域化相位在何种条件下能够在这种全局耦合下存活，目前仍不清楚。我们研究了无序伊辛模型中的能量依赖局域化，该模型具有横向和纵向场，并全局耦合到一个d能级系统（qudit）。引人注目的是，我们发现了一个倒置的迁移率边，其中高能态是局域化的，而低能态是退局域化的。我们的结果得到了shift-and-invert本征态定位和Krylov时间演化的支持，分别达到L=13和L=18。我们论证了局域化相变的临界能量按E_c ∝ L^{1/2}标度，这与有限尺寸数值结果一致。我们还展示了在更低能量下存在重入多体局域化（MBL）相的证据，尽管在该区域中心模式具有强效应。类似的结果应出现在大S的中心自旋-S问题以及某些腔QED模型中。
英文摘要：
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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