Signatures of integrability in the dynamics of Rydberg-blockaded chains

Abstract

A recent experiment on a 51-atom Rydberg blockaded chain observed anomalously long-lived temporal oscillations of local observables after quenching from an antiferromagnetic initial state. This coherence is surprising as the initial state should have thermalized rapidly to infinite temperature. In this article, we show that the experimental Hamiltonian exhibits non-thermal behavior across its entire many-body spectrum, with similar finite-size scaling properties as models proximate to integrable points. Moreover, we construct an explicit small local deformation of the Hamiltonian which enhances both the signatures of integrability and the coherent oscillations observed after the quench. Our results suggest that a parent proximate integrable point controls the early-to-intermediate time dynamics of the experimental system. The distinctive quench dynamics in the parent model could signal an unconventional class of integrable system.Introduction-Remarkable experimental advances in the construction and control of synthetic quantum systems [1][2][3][4][5][6][7][8][9][10][11][12][13][14] have revived interest in foundational questions about quantum thermalization and the emergence of statistical mechanics [15][16][17]. Experiments have observed robust thermalization when the interactions are strong, localization and the concomitant persistence of initial state memory when spatial inhomogeneities are strong, and long-lived prethermal states near special integrable points [4][5][6][7][8][9][10][11][12][13][14].Conventional wisdom holds that generic, strongly interacting isolated systems quickly reach local thermal equilibrium at infinite temperature, irrespective of the initial state [15][16][17]. It therefore came as a surprise when recent quench experiments in long Rydberg-blockaded atomic chains reported a strong initial state dependence in infinite temperature thermalization times [12]. In the Rydberg-blockaded regime, the effective dynamics occurs in a constrained manifold as adjacent atoms cannot simultaneously support Rydberg excitations. The experiment observed long-lived coherent oscillations in local observables starting from a Neél state with the maximum number of Rydberg excitations (called |Z 2 ), but fast relaxation starting from a state with no Rydberg excitations (|0 ). What is the source of this coherence at infinite temperature?In this Rapid Communication, we provide a partial answer by identifying signatures of integrability in the Hamiltonian controlling the time-evolution (H 0 in Eq. (1)). Specifically, we construct a deformation of H 0 that both magnifies the amplitude and lifetime of the coherent oscillations observed in quenches, and monotonically enhances various spectral signatures of integrability. From our study, we hypothesize that a parent nonergodic point that is proximate in parameter space to H 0 controls its short-time dynamics and small system-size eigenspectra. This parent point is a new model in constrained systems that has not been previously studied; although it is exhibits various ...

Quantum scars as embeddings of weakly broken Lie algebra representations

“…Throughout this paper, all optimizations were carried out using the built-in Python minimization routine that uses SLSQP method. Afer optimization, we recover the perturbation that was previously empirically found 49 to enhance the revivals following a |Z 2 quench with maximal f 0 when λ = 0.108 (at system size N = 18). It was previously demonstrated the PXP model remains nonintegrable after including this perturbation.…”

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

“…Rydbergblockaded chains) could be extremely slow, if prepared in specific experimentally accessible out-of-equilibrium initial states [37][38][39][40][41][42] . This reminiscence of integrable behavior for the dynamics of certain initial states is believed to be captured by a set of eigenstates of measure zero, which violates ETH 39,40,42,43 and have a considerable big overlap with these initial states. Importantly, these atypical eigenstates are even at infinite temperature distributed through the whole spectrum, such that they are embedded into a sea of thermal states.…”

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