Efficiently solving the dynamics of many-body localized systems at strong disorder

Tomasi, Giuseppe De; Pollmann, Frank; Heyl, Markus

doi:10.1103/physrevb.99.241114

Cited by 63 publications

(70 citation statements)

References 85 publications

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“…However, the block structure of the Hamiltonian itself does not put any constraints of the amount of entanglement it can generate. In particular, even a unitary made up entirely by random diagonal phases in the z-basis can generate the same amount of entanglement as a Haar random unitary, when applied to a state that is an equal weight superposition of all basis states 19 [92]. This point is also illustrated by considering the t−J z model.…”

Section: Entanglement Growthmentioning

confidence: 92%

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: Entanglement Growthmentioning

confidence: 92%

Statistical localization: From strong fragmentation to strong edge modes

et al. 2020

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“…Monitoring temporal fluctuations of a local operator can be seen as a measure for attainable volume that an initial excitation can explore. In Anderson localized systems, temporal fluctuations never vanish [81] since the effective volume is strictly limited by the localization length, seen in Fig. 8(b) (dashed line).…”

Section: B Dynamics Of On-site Number Fluctuationsmentioning

confidence: 98%

“…Such observables are more accessible in experiments. One possibility is to study temporal fluctuations of local observables [80,81]. We consider here dynamics of fluctuations for the number operatorn of the -th site, defined as…”

Section: B Dynamics Of On-site Number Fluctuationsmentioning

confidence: 99%

“…being a signal that after the initial build-up of the localization wave function the effective volume is slowly expanding [80,81]. Curiously, there is a clear distinction at later times between the power law like decay in the many-body localized phase and the saturation in the Anderson localized phase, but this distinction becomes visible roughly one order of magnitude later than in the bipartite entanglement entropy.…”

Section: B Dynamics Of On-site Number Fluctuationsmentioning

confidence: 99%

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Probing the many-body localization phase transition with superconducting circuits

et al. 2019

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Chains of superconducting circuit devices provide a natural platform for studies of synthetic bosonic quantum matter. Motivated by the recent experimental progress in realizing disordered and interacting chains of superconducting transmon devices, we study the bosonic many-body localization phase transition using the methods of exact diagonalization as well as matrix product state dynamics. We estimate the location of transition separating the ergodic and the many-body localized phases as a function of the disorder strength and the many-body on-site interaction strength. The main difference between the bosonic model realized by superconducting circuits and similar fermionic model is that the effect of the on-site interaction is stronger due to the possibility of multiple excitations occupying the same site. The phase transition is found to be robust upon including longer-range hopping and interaction terms present in the experiments. Furthermore, we calculate experimentally relevant local observables and show that their temporal fluctuations can be used to distinguish between the dynamics of Anderson insulator, many-body localization, and delocalized phases. While we consider unitary dynamics, neglecting the effects of dissipation, decoherence and measurement back action, the timescales on which the dynamics is unitary are sufficient for observation of characteristic dynamics in the many-body localized phase. Moreover, the experimentally available disorder strength and interactions allow for tuning the many-body localization phase transition, thus making the arrays of superconducting circuit devices a promising platform for exploring localization physics and phase transition.

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“…Although, the eigenstates in an MBL phase do not present substantial difference with the one of an Anderson insulator (V = 0), for instance, entanglement properties, the dynamics of an MBL phase is much richer. Interactions induce a dephasing which allows slow logarithmic information propagation through the system, even though particle and energy transport is absence 20,96,97 . We compute the evolution of the bipartite entanglement entropy S(t) after quenching a random product state |ψ = xĉ † x |0 that belongs to the largest block ofĤ ∞ .…”

Section: B Dynamicsmentioning

confidence: 99%

Dynamics of strongly interacting systems: From Fock-space fragmentation to many-body localization

et al. 2019

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We study the t−V disordered spinless fermionic chain in the strong coupling regime, t/V → 0. Strong interactions highly hinder the dynamics of the model, fragmenting its Hilbert space into exponentially many blocks in system size. Macroscopically, these blocks can be characterized by the number of new degrees of freedom, which we refer to as movers. We focus on two limiting cases: blocks with only one mover and the ones with a finite density of movers. The former many-particle block can be exactly mapped to a single-particle Anderson model with correlated disorder in one dimension. As a result, these eigenstates are always localized for any finite amount of disorder. The blocks with a finite density of movers, on the other side, show an MBL transition that is tuned by the disorder strength. Moreover, we provide numerical evidence that its ergodic phase is diffusive at weak disorder. Approaching the MBL transition, we observe sub-diffusive dynamics at finite time scales and find indications that this might be only a transient behavior before crossing over to diffusion. arXiv:1909.03073v1 [cond-mat.dis-nn]

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Efficiently solving the dynamics of many-body localized systems at strong disorder

Cited by 63 publications

References 85 publications

Statistical localization: From strong fragmentation to strong edge modes

Statistical localization: From strong fragmentation to strong edge modes

Probing the many-body localization phase transition with superconducting circuits

Dynamics of strongly interacting systems: From Fock-space fragmentation to many-body localization

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