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arXiv:2204.13718 · Physical review. B./Physical review. B

Driving quantum many-body scars in the PXP model

Ana Hudomal, Jean-Yves Desaules, Bhaskar Mukherjee, Guo-Xian Su, Jad C. Halimeh, Zlatko Papić

Published Sep 2, 2022• 44 citations
arXivHTMLPDF

Abstract

Periodic driving has been established as a powerful technique for engineering novel phases of matter and intrinsically out-of-equilibrium phenomena such as time crystals. Recent paper by Bluvstein et al. [Science 371, 1355 (2021)] has demonstrated that periodic driving can also lead to a significant enhancement of quantum many-body scarring, whereby certain nonintegrable systems can display persistent quantum revivals from special initial states. Nevertheless, the mechanisms behind driving-induced scar enhancement remain poorly understood. Here we report a detailed study of the effect of periodic driving on the PXP model describing Rydberg atoms in the presence of a strong Rydberg blockade---the canonical static model of quantum many-body scarring. We show that periodic modulation of the chemical potential gives rise to a rich phase diagram, with at least two distinct types of scarring regimes that we distinguish by examining their Floquet spectra. We formulate a toy model, based on a sequence of square pulses, that accurately captures the details of the scarred dynamics and allows for analytical treatment in the large-amplitude and high-frequency driving regimes. Finally, we point out that driving with a spatially inhomogeneous chemical potential allows to stabilize quantum revivals from arbitrary initial states in the PXP model, via a mechanism similar to prethermalization.

DOI
10.1103/physrevb.106.104302

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Periodic driving has been established as a powerful technique for engineering novel phases of matter and intrinsically out-of-equilibrium phenomena such as time crystals. Recent paper by Bluvstein et al. [Science 371, 1355 (2021)] has demonstrated that periodic driving can also lead to a significant enhancement of quantum many-body scarring, whereby certain nonintegrable systems can display persistent quantum revivals from special initial states. Nevertheless, the mechanisms behind driving-induced scar enhancement remain poorly understood. Here we report a detailed study of the effect of periodic driving on the PXP model describing Rydberg atoms in the presence of a strong Rydberg blockade---the canonical static model of quantum many-body scarring. We show that periodic modulation of the chemical potential gives rise to a rich phase diagram, with at least two distinct types of scarring regimes that we distinguish by examining their Floquet spectra. We formulate a toy model, based on a sequence of square pulses, that accurately captures the details of the scarred dynamics and allows for analytical treatment in the large-amplitude and high-frequency driving regimes. Finally, we point out that driving with a spatially inhomogeneous chemical potential allows to stabilize quantum revivals from arbitrary initial states in the PXP model, via a mechanism similar to prethermalization.
The PXP model hosts a special set of nonergodic states, referred to as quantum many-body scars. One of the consequences of quantum scarring is the periodic revival of the wave function fidelity. It has been reported that quantum fidelity revival occurs in the PXP model for certain product states, and periodic driving of the chemical potential can enhance the magnitude of quantum revival and can even change the frequencies of revival showing the subharmonic response. Although the effect of the periodic driving in the PXP model has been studied in the limit of certain perturbative regimes, the general mechanism of such enhanced revival and frequency change has been barely studied. In this paper, we investigate how periodic driving in the PXP model can systematically control the fidelity revival. Particularly, focusing on a product state called the N\'eel state, we analyze the condition of driving to enhance the magnitude of revival or change the frequencies of revival. To clarify the reason for such control, we consider the similarities between the PXP model and the free spin-1/21/21/2 model in graph theoretical analysis and show that the quantum fidelity feature in the PXP model is well explained by the free spin-1/21/21/2 model. In addition, under a certain limit of the driving parameters, an analytic approach to explain the main features of the fidelity revival is also applied. Our results give insight into the scarring nature of the periodically driven PXP model and pave the way to understand the (sub)harmonic responses in these models and controls thereof.
The control of many-body quantum dynamics in complex systems is a key challenge in the quest to reliably produce and manipulate large-scale quantum entangled states. Recently, quench experiments in Rydberg atom arrays [Bluvstein et al. Science 371, 1355 (2021)SCIEAS0036-807510.1126/science.abg2530] demonstrated that coherent revivals associated with quantum many-body scars can be stabilized by periodic driving, generating stable subharmonic responses over a wide parameter regime. We analyze a simple, related model where these phenomena originate from spatiotemporal ordering in an effective Floquet unitary, corresponding to discrete time-crystalline behavior in a prethermal regime. Unlike conventional discrete time crystals, the subharmonic response exists only for Néel-like initial states, associated with quantum scars. We predict robustness to perturbations and identify emergent timescales that could be observed in future experiments. Our results suggest a route to controlling entanglement in interacting quantum systems by combining periodic driving with many-body scars.
Quantum dynamics in certain kinetically-constrained systems can display a strong sensitivity to the initial condition, wherein some initial states give rise to persistent quantum revivals---a type of weak ergodicity breaking known as ``quantum many-body scarring'' (QMBS). Recent work [Yao, Pan, Liu, and Zhai, Phys. Rev. B 105, 125123 (2022)] pointed out that QMBS gets destroyed by tuning the system to a quantum critical point, echoing the disappearance of long-range order in the system's ground state at equilibrium. Here we show that this picture can be much richer in systems that display QMBS dynamics from a continuous family of initial conditions: As the system is tuned across the critical point while at the same time deforming the initial state, the dynamical signatures of QMBS at intermediate times can undergo an apparently smooth evolution across the equilibrium phase transition point. We demonstrate this using the PXP model---a paradigmatic model of QMBS that has recently been realized in Rydberg atom arrays as well as ultracold bosonic atoms in a tilted optical lattice. Using exact diagonalization and matrix product state methods, we map out the dynamical phase diagram of the PXP model with the quenched chemical potential. We demonstrate the existence of a continuous family of initial states that give rise to QMBS and formulate a ramping protocol that can be used to prepare such states in experiment. Our results show the ubiquity of scarring in the PXP model and highlight its intriguing interplay with quantum criticality.
We propose a scheme that generates period-doubled responses via periodically driving certain Hamiltonians hosting quantum many-body scars, akin to recent experimental observations in driven Rydberg atom arrays. Our construction takes advantage of an su(2) spectrum generating algebra associated with the static quantum-scarred Hamiltonian, which enacts a $\ensuremath{\pi}$ rotation within the scar subspace after one period of time evolution with appropriately chosen driving parameters. This yields period-doubled (subharmonic) responses in local observables for any choice of initial state residing in the scar subspace. The quasienergy spectrum features atypical $\ensuremath{\pi}$-paired eigenstates embedded in an otherwise fully thermal spectrum. The protocol requires neither a large driving frequency nor a large driving amplitude and is thus distinct from the prethermalization physics in previous investigations of the driven PXP model. We demonstrate our scheme using several spin-1/2 and spin-1 quantum scarred models possessing an exact su(2) spectrum generating algebra, as well as a symmetry-deformed PXP model, where the su(2) algebra is only approximate. Our results extend the class of models hosting quantum many-body scars that can be leveraged to yield time-crystalline behaviors under periodic driving.
Motivated by recent experiments realizing long-lived nonequilibrium states in aperiodically driven quantum many-body systems, we investigate the dynamics of a quasiperiodically driven Rydberg atom chain in the strong Rydberg blockage regime. In this regime, the system is kinetically constrained and the ``PXP'' model describes its dynamics. Even without driving, the PXP model exhibits many-body scarring and resultant persistent oscillations for dynamics originating from the N\'eel-ordered initial state. We demonstrate that a rich array of dynamical behaviors emerge when the system is subjected to a continuous drive. In the high-frequency regime, the system exhibits revivals and oscillations for the N\'eel ordered initial state both for periodic and quasiperiodic drives. We trace the origin of this nonergodicity to an effective PXP Hamiltonian for both of these driving protocols in this regime. Furthermore, we demonstrate that the behavior of the fidelity and the entanglement entropy is nonmonotonic at low frequencies in the high-amplitude regime. This leads to several re-entrant scarring transitions both for both the N\'eel-ordered and the fully polarized initial state. Our results demonstrate that continuous quasiperiodic drive protocols can provide a promising route to realize prethermal phases of matter in kinetically constrained systems.
Persistent revivals recently observed in Rydberg atom simulators have challenged our understanding of thermalization and attracted much interest to the concept of quantum many-body scars (QMBSs). QMBSs are non-thermal highly excited eigenstates that coexist with typical eigenstates in the spectrum of many-body Hamiltonians, and have since been reported in multiple theoretical models, including the so-called PXP model, approximately realized by Rydberg simulators. At the same time, questions of how common QMBSs are and in what models they are physically realized remain open. In this Letter, we demonstrate that QMBSs exist in a broader family of models that includes and generalizes PXP to longer-range constraints and states with different periodicity. We show that in each model, multiple QMBS families can be found. Each of them relies on a different approximate su(2) algebra, leading to oscillatory dynamics in all cases. However, in contrast to the PXP model, their observation requires launching dynamics from weakly entangled initial states rather than from a product state. QMBSs reported here may be experimentally probed using Rydberg atom simulator in the regime of longer-range Rydberg blockades.