Stark Many-Body Localization

Schulz, Maximilian; Hooley, C.; Moessner, Roderich; Pollmann, Frank

doi:10.1103/physrevlett.122.040606

Cited by 250 publications

(276 citation statements)

References 33 publications

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“…In the following, we take open boundary conditions. Such dipoleconserving Hamiltonians appear as effective descriptions in a variety of settings, such as fracton systems [49,86], the quantum Hall effect [47,[87][88][89][90], and for charged particles in a strong electric field [32,91].…”

Section: Dipole-conserving Hamiltonian H3mentioning

confidence: 99%

Statistical localization: From strong fragmentation to strong edge modes

et al. 2020

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Certain disorder-free Hamiltonians can be non-ergodic due to a strong fragmentation of the Hilbert space into disconnected sectors. Here, we characterize such systems by introducing the notion of 'statistically localized integrals of motion' (SLIOM), whose eigenvalues label the connected components of the Hilbert space. SLIOMs are not spatially localized in the operator sense, but appear localized to sub-extensive regions when their expectation value is taken in typical states with a finite density of particles. We illustrate this general concept on several Hamiltonians, both with and without dipole conservation. Furthermore, we demonstrate that there exist perturbations which destroy these integrals of motion in the bulk of the system, while keeping them on the boundary. This results in statistically localized strong zero modes, leading to infinitely long-lived edge magnetizations along with a thermalizing bulk, constituting the first example of such strong edge modes in a non-integrable model. We also show that in a particular example, these edge modes lead to the appearance of topological string order in a certain subset of highly excited eigenstates. Some of our suggested models can be realized in Rydberg quantum simulators.CONTENTS * These authors contributed equally to this work.

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Section: Dipole-conserving Hamiltonian H3mentioning

confidence: 99%

Statistical localization: From strong fragmentation to strong edge modes

et al. 2020

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“…Until recently, most of the theoretical studies have focused on MBL induced by the disorders encoded in the on-site potentials, hopping amplitudes and interactions, as well as quasi-periodic potentials [13]. On the other hand very recently, disorder-free AL/MBL-like phenomena have been revealed in a Wannier-Stark ladder [14][15][16], dipolar atom gases in an optical lattice [17], some lattice-gauge theoretical models [18][19][20][21], quantum Hall systems [22], a diamond chain system [23][24][25], and a disorder-free spin chain [26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Flat-band many-body localization and ergodicity breaking in the Creutz ladder

2020

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We study disorder-free many-body localization in the flat-band Creutz ladder, which was recently realized in cold-atoms in an optical lattice. In a non-interacting case, the flat-band structure of the system leads to a Wannier wavefunction localized on four adjacent lattice sites. In the flat-band regime both with and without interactions, the level spacing analysis exhibits Poisson-like distribution indicating the existence of disorder-free localization. Calculations of the inverse participation ratio support this observation. Interestingly, this type of localization is robust to weak disorders, whereas for strong disorders, the system exhibits a crossover into the conventional disorder-induced manybody localizated phase. Physical picture of this crossover is investigated in detail. We also observe nonergodic dynamics in the flat-band regime without disorder. The memory of an initial density wave pattern is preserved for long times.

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“…Finally, we examine the entanglement entropy and participation ratio of the undriven Heisenberg spin chain with magnetic field gradient. These quantities have been studied previously for disordered Heisenberg spin chains [16,46,47] and for spinless fermions in an electric field [24,25], the latter being equivalent to a spin chain with a gradient. We make a direct comparison to these earlier works in Appendix C. Here, we instead focus on the gradient dependence of these diagnostics in parameter regimes relevant for QD experiments.…”

Section: Many-body Localizationmentioning

confidence: 99%

“…Here we present further results for the MBL phase in the gradient field model, with the goal of comparing more directly with previous work [24,25]. To this end, in the present section we sample the local field disorder from the uniform distribution [−δB, δB], as in Ref.…”

Section: Appendix C: Mbl Signatures: Comparison With the Literaturementioning

confidence: 99%

Discrete time crystal in the gradient-field Heisenberg model

Dyke

Warren

et al. 2020

Phys. Rev. B

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We show that time crystal phases, which are known to exist for disorder-based many-body localized systems, also appear in systems where localization is due to strong magnetic field gradients. Specifically, we study a finite Heisenberg spin chain in the presence of a gradient field, which can be realized experimentally in quantum dot systems using micromagnets or nuclear spin polarization. Our numerical simulations reveal time crystalline order over a broad range of realistic quantum dot parameters, as evidenced by the long-time preservation of spin expectation values and the asymptotic form of the mutual information. We also consider the undriven system and present several diagnostics for many-body localization that are complementary to those recently studied. Our results show that these non-ergodic phases should be realizable in modest-sized quantum dot spin arrays using only demonstrated experimental capabilities. arXiv:1912.05130v1 [quant-ph]

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Stark Many-Body Localization

Cited by 250 publications

References 33 publications

Statistical localization: From strong fragmentation to strong edge modes

Statistical localization: From strong fragmentation to strong edge modes

Flat-band many-body localization and ergodicity breaking in the Creutz ladder

Discrete time crystal in the gradient-field Heisenberg model

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