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

Abstract

We study the dynamics of an interacting quantum spin chain under the application of a linearly increasing potential. This model exhibits a type of localization known as Stark many-body localization. The dynamics shows a strong dependence on the initial conditions, indicating that the system violates the eigenstate thermalization hypothesis at any finite gradient of the potential. This is contrary to reports of a numerically observed ergodic phase. Therefore, the localization is crucially distinct from disorder-driven many-body localization, in agreement with recent predictions on the basis of localization via Hilbert-space shattering.

Observation of Stark many-body localization without disorder

“…These conservation laws result in localization, but the localized regions still have interactions with one another, resulting in slow spreading of correlations via entanglement after a quench from a product state (typically logarithmic spreading in time, but potentially faster for long-range interactions [39]). While the existence of similar conserved quantities in Stark MBL is debated [23,24], there are indications that it can display similar entanglement dynamics [5,18]. Some observables have been established to directly probe this correlation spreading, such as quantum Fisher information [27,28] (see Methods and Extended Data Fig.…”

“…From this, it has been predicted that interacting systems with a strong linear tilt can also display MBL-like behavior [4,5]. This effect, sometimes called Stark MBL, has attracted considerable theoretical and experimental interest [18][19][20][21][22][23][24][25][26][27]. However, clear experimental realization of Stark MBL has been complicated by exact degeneracies between states with the same center of mass that occur * wmorong@umd.edu in the limit of short-range interactions [4,5,26].…”

Many-body localization in tilted and harmonic potentials

“…On the other hand, the tilted lattice, due to shattered Hilbert space [28,29], supports long-lived nonergodic states in form of extended domains as pointed out in [44] also for relatively small tilt when the majority of separable initial states thermalizes fast. Their existence may be traced back to a peculiar feature of the Heisenberg model -the domain containing spins with the same orientation (up or down oriented spins) is practically frozen in the dynamics for the time dependent on the length of the domain.…”

“…While [35] averaged the dynamics over different possible states, we choose the Néel state that corresponds, after Jordan-Wigner transformation, to an equivalent density wave state with every second site being occupied and other being empty in the spinless fermion representation in analogy to the experimental situation [25]. This also allows us to avoid states with extended domains [44,45] that may results in atypical localization due to frozen spins.…”

“…Their existence may be traced back to a peculiar feature of the Heisenberg model -the domain containing spins with the same orientation (up or down oriented spins) is practically frozen in the dynamics for the time dependent on the length of the domain. So local thermalization occurs at domain wall only [44,45].…”