Stark many-body localization: Evidence for Hilbert-space shattering

Hilbert space shattering and disorder-free localization in polar lattice gases

Emerging dynamical constraints resulting from inter-site interactions severely limit particle mobility in polar lattice gases. Whereas in absence of disorder hard-core Hubbard models with only strong nearest-neighbor interactions present Hilbert space fragmentation but no many-body localization for typical states, the $1/r^3$ tail of the dipolar interaction results in Hilbert space shattering, as well as in a dramatically slowed down dynamics and eventual disorder-free localization. Our results show that the study of the intriguing interplay between disorder- and interaction-induced many-body …

Hilbert space shattering and dynamical freezing in the quantum Ising model

We discuss quantum dynamics in the transverse field Ising model in two spatial dimensions. We show that, up to a prethermal timescale, which we quantify, the Hilbert space 'shatters' into dynamically disconnected subsectors. We identify this shattering as originating from the interplay of a $\mathrm{U}(1)$ conservation law and a one-form $\mathbb{Z}_2$ constraint. We show that the number of dynamically disconnected sectors is exponential in system volume, and includes a subspace exponential in system volume within which the dynamics is exactly localized, even in the absence of quenched disorde…

Localization from Hilbert space shattering: from theory to physical realizations

We show how a finite number of conservation laws can globally `shatter' Hilbert space into exponentially many dynamically disconnected subsectors, leading to an unexpected dynamics with features reminiscent of both many body localization and quantum scars. A crisp example of this phenomenon is provided by a `fractonic' model of quantum dynamics constrained to conserve both charge and dipole moment. We show how the Hilbert space of the fractonic model dynamically fractures into disconnected emergent subsectors within a particular charge and dipole symmetry sector. This shattering can occur in a…

Hilbert-space fragmentation, multifractality, and many-body localization

Investigating many-body localization (MBL) using exact numerical methods is limited by the exponentialgrowth of the Hilbert space. However, localized eigenstates display multifractality and only extend over a vanishing fraction of the Hilbert space. Here, building on this remarkable property, we develop a simple yet efficient decimation scheme to discard the irrelevant parts of the Hilbert space of the random-field Heisenberg chain. This leads to an Hilbert space fragmentation in small clusters, allowing to access larger systems at strong disorder. The MBL transition is quantitatively predicte…

Experimental probes of Stark many-body localization

Recent work has focused on exploring many-body localization (MBL) in systems without quenched disorder: one such proposal is Stark MBL in which small perturbations to a strong linear potential yield localization. However, as with conventional MBL, it is challenging to experimentally distinguish between non-interacting localization and true MBL. In this paper we show that several existing experimental probes, designed specifically to differentiate between these scenarios, work similarly in the Stark MBL setting. In particular we show that a modified spin-echo response (DEER) shows clear signs o…

具有长程相互作用的 Stark 多体局域化

Stark many-body localization with long-range interactions

本文研究一维无自旋费米子中长程相互作用对 Stark MBL 的影响，通过相图和 TDVP 动力学揭示强相互作用下系统始终局域化且 Hilbert 空间碎片化抑制热化。