Quantum many-body scars from magnon condensation

Iadecola, Thomas; Schecter, Michael; Xu, Shenglong

doi:10.1103/physrevb.100.184312

Cited by 148 publications

(125 citation statements)

References 62 publications

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“…By contrast, in the strongly interacting Rydberg atom chain initialized in the Néel state, quantum dynamics remains concentrated around a small subset of states in the many-body Hilbert space, thus it is effectively "semiclassical" [21]. While recent works [26,27] have shown that revivals can be significantly enhanced by certain perturbations to the system, a general understanding of the conditions that allow scars to occur in a many-body quantum system is still lacking.The observation of periodic dynamics was linked to the existence of atypical eigenstates at evenly spaced energies throughout the spectrum of the many-body system [20,28,29]. Similar phenomenology was previously found in the non-integrable AKLT model [30,31], where highly-excited eigenstates with low entanglement have been analytically constructed.…”

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confidence: 68%

Systematic Construction of Scarred Many-Body Dynamics in 1D Lattice Models

2019

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We introduce a family of non-integrable 1D lattice models that feature robust periodic revivals under a global quench from certain initial product states, thus generalizing the phenomenon of many-body scarring recently observed in Rydberg atom quantum simulators. Our construction is based on a systematic embedding of the single-site unitary dynamics into a kinetically-constrained many-body system. We numerically demonstrate that this construction yields new families of models with robust wave-function revivals, and it includes kinetically-constrained quantum clock models as a special case. We show that scarring dynamics in these models can be decomposed into a period of nearly free clock precession and an interacting bottleneck, shedding light on their anomalously slow thermalization when quenched from special initial states.Introduction.-The understanding of ergodicity and thermalization in isolated quantum systems is an open problem in many-body physics, with important implications for a variety of experimental systems [1][2][3][4][5]. On the one hand, this problem has inspired important developments such as Eigenstate Thermalization Hypothesis (ETH) [6][7][8], which establishes a link between ergodicity and the properties of the system's eigenstates. On the other hand, strong violation of ergodicity can result in rich new physics, such as in integrable systems [9], Anderson insulators [10], and many-body localized phases [11][12][13]. In these cases, the emergence of many conservation laws prevents the system, initialized in a random state, from fully exploring all allowed configurations in the Hilbert space, causing a strong ergodicity breaking.A recent experiment on an interacting quantum simulator [14] has reported a surprising observation of quantum dynamics that is suggestive of weak ergodicity breaking. Utilizing large 1D chains of Rydberg atoms [14-16], the experiment showed that quenching the system from a Néel initial state lead to persistent revivals of local observables, while other initial states exhibited fast equilibration without any revivals. The stark sensitivity of the system's dynamics to the initial states, which were all effectively drawn from an "infinite temperature" ensemble, appeared at odds with "strong" ETH [17][18][19].In Ref. 20 and 21 the non-ergodic dynamics of a Rydberg atom chain was interpreted as a many-body generalization of the classic phenomenon of quantum scar [22]. For a quantum particle in a stadium billiard, scars represent an anomalous concentration of the particle's trajectory around (unstable) periodic orbits in the corresponding classical system, which has an impact on optical and transport properties [23][24][25]. By contrast, in the strongly interacting Rydberg atom chain initialized in the Néel state, quantum dynamics remains concentrated around a small subset of states in the many-body Hilbert space, thus it is effectively "semiclassical" [21]. While recent works [26,27] have shown that revivals can be significantly enhanced by certain perturbations to the syst...

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confidence: 68%

Systematic Construction of Scarred Many-Body Dynamics in 1D Lattice Models

2019

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“…Recently, however, several exceptions have been discovered [34][35][36][37][38]. Systems with constrained dynamics [39,40] are an especially promising avenue where non-thermal eigenstates, dubbed scar states, can occur [33,[41][42][43][44][45].…”

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confidence: 99%

Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians

et al. 2020

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We show that the combination of charge and dipole conservation-characteristic of fracton systems-leads to an extensive fragmentation of the Hilbert space, which in turn can lead to a breakdown of thermalization. As a concrete example, we investigate the out-of-equilibrium dynamics of one-dimensional spin-1 models that conserve charge (total S z ) and its associated dipole moment. First, we consider a minimal model including only three-site terms and find that the infinite temperature auto-correlation saturates to a finite value-showcasing non-thermal behavior. The absence of thermalization is identified as a consequence of the strong fragmentation of the Hilbert space into exponentially many invariant subspaces in the local S z basis, arising from the interplay of dipole conservation and local interactions. Second, we extend the model by including four-site terms and find that this perturbation leads to a weak fragmentation: the system still has exponentially many invariant subspaces, but they are no longer sufficient to avoid thermalization for typical initial states. More generally, for any finite range of interactions, the system still exhibits non-thermal eigenstates appearing throughout the entire spectrum. We compare our results to charge and dipole moment conserving random unitary circuit models for which we reach identical conclusions.arXiv:1904.04266v2 [cond-mat.str-el]

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“…Several works investigated the possibility of mimicking similarly localized behavior without explicitly breaking translation invariance [25][26][27][28][29][30][31][32][33], as well as the possibility of intermediate behavior, such as the existence of a small number of ETH-violating eigenstates within an otherwise generic spectrum of states [34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. Recently, the authors of the present paper, following earlier work on dipole-conserving random circuits [49], identified a novel mechanism for such non-ergodic behavior, dubbed Hilbert space fragmentation [50,51].…”

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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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Quantum many-body scars from magnon condensation

Cited by 148 publications

References 62 publications

Systematic Construction of Scarred Many-Body Dynamics in 1D Lattice Models

Systematic Construction of Scarred Many-Body Dynamics in 1D Lattice Models

Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians

Statistical localization: From strong fragmentation to strong edge modes

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