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

Tomasi, Giuseppe De; Hetterich, Daniel; Sala, Pablo; Pollmann, Frank

doi:10.1103/physrevb.100.214313

Cited by 110 publications

(81 citation statements)

References 104 publications

(189 reference statements)

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“…More generally, it would be interesting to investigate the role SLIOMs play in a many body localized phase, both at the boundary and in the bulk. In fact, recent works [36,93] investigated the MBL transition for models, which one could try to describe in the language of SLIOMs. It would also be interesting to look for other models exhibiting SLIOMs, either at their boundary or in their bulk.…”

Section: Discussionmentioning

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: Discussionmentioning

confidence: 99%

Statistical localization: From strong fragmentation to strong edge modes

et al. 2020

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“…Nevertheless, since the problem is fundamentally a many-body one, the underlying Fock space offers a seemingly natural framework within which to study and understand it [32][33][34][35][36][37][38][39][40][41][42][43]. More recently, it has been shown that this is indeed the case.…”

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confidence: 99%

Fock-space correlations and the origins of many-body localization

Roy

Logan

2020

Phys. Rev. B

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We consider the problem of many-body localisation on Fock space, focussing on the essential features of the Hamiltonian which stabilise a localised phase. Any many-body Hamiltonian has a canonical representation as a disordered tight-binding model on the Fock-space graph. The underlying physics is however fundamentally different from that of conventional Anderson localisation on high-dimensional graphs because the Fock-space graph possesses non-trivial correlations. These correlations are shown to lie at the heart of whether or not a stable many-body localised phase can be sustained in the thermodynamic limit, and a theory is presented for the conditions the correlations must satisfy for a localised phase to be stable. Our analysis is rooted in a probabilistic, self-consistent mean-field theory for the local Fock-space propagator and its associated self-energy; in which the Fock-space correlations, together with the extensive nature of the connectivity of Fock-space nodes, are key ingredients. The origins of many-body localisation in typical local Hamiltonians where the correlations are strong, as well as its absence in uncorrelated random energy-like models, emerge as predictions from the same overarching theory. To test these, we consider three specific microscopic models, first establishing in each case the nature of the associated Fock-space correlations. Numerical exact diagonalisation is then used to corroborate the theoretical predictions for the occurrence or otherwise of a stable many-body localised phase; with mutual agreement found in each case. CONTENTS

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“…More recently still, several models were found, where the many-body spectrum is sprinkled with highly athermal states that, by the nature of many-body spectra, live nearby in energy to thermal states in the middle of the spectrum [21][22][23][24][25][26][26][27][28][29][30][31][32][33][34][35][36][37]. These unusual states are called many-body scars.…”

Section: Introductionmentioning

confidence: 99%

Information dynamics in a model with Hilbert space fragmentation

2021

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The fully frustrated ladder – a quasi-1D geometrically frustrated spin one half Heisenberg model – is non-integrable with local conserved quantities on rungs of the ladder, inducing the local fragmentation of the Hilbert space into sectors composed of singlets and triplets on rungs. We explore the far-from-equilibrium dynamics of this model through the entanglement entropy and out-of-time-ordered correlators (OTOC). The post-quench dynamics of the entanglement entropy is highly anomalous as it shows clear non-damped revivals that emerge from short connected chunks of triplets. We find that the maximum value of the entropy follows from a picture where coherences between different fragments co-exist with perfect thermalization within each fragment. This means that the eigenstate thermalization hypothesis holds within all sufficiently large Hilbert space fragments. The OTOC shows short distance oscillations arising from short coupled fragments, which become decoherent at longer distances, and a sub-ballistic spreading and long distance exponential decay stemming from an emergent length scale tied to fragmentation.

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

Cited by 110 publications

References 104 publications

Statistical localization: From strong fragmentation to strong edge modes

Statistical localization: From strong fragmentation to strong edge modes

Fock-space correlations and the origins of many-body localization

Information dynamics in a model with Hilbert space fragmentation

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