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arXiv:1911.06092 · Physical Review Research

Many-body scar state intrinsic to periodically driven system

Sho Sugiura, Tomotaka Kuwahara, Keiji Saito

Published Feb 2, 2021• 62 citations
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Abstract

The violation of the Floquet version of the eigenstate thermalization hypothesis is rigorously discussed with realistic Hamiltonians.Our model is based on the PXP-type interactions without disorder.We rigorously prove the existence of many-body scar states in the Floquet eigenstates that appear only at specific periods of driving by showing the explicit expressions of the wave functions.This is equivalently the first rigorous proof of the breakdown of the Floquet eigenstate thermalization hypothesis.Through the exact expression of the scar states, the underlying physical mechanism is clarified.Using the underlying mechanism, various driven Hamiltonians with Floquet-scar states can be systematically engineered.We then discuss Floquet-scar states that can be checked through time evolution of observables in a chain of Rydberg atoms.

DOI
10.1103/physrevresearch.3.l012010

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The violation of the Floquet version of the eigenstate thermalization hypothesis is rigorously discussed with realistic Hamiltonians.Our model is based on the PXP-type interactions without disorder.We rigorously prove the existence of many-body scar states in the Floquet eigenstates that appear only at specific periods of driving by showing the explicit expressions of the wave functions.This is equivalently the first rigorous proof of the breakdown of the Floquet eigenstate thermalization hypothesis.Through the exact expression of the scar states, the underlying physical mechanism is clarified.Using the underlying mechanism, various driven Hamiltonians with Floquet-scar states can be systematically engineered.We then discuss Floquet-scar states that can be checked through time evolution of observables in a chain of Rydberg atoms.
The presence of quantum scars, athermal eigenstates of a many-body Hamiltonian with finite-energy density, leads to an absence of ergodicity and long-time coherent dynamics starting from initial states that have a high overlap with scars as experimentally observed in a chain of ultracold Rydberg atoms. We show, via study of a periodically driven Rydberg chain, that the drive frequency acts as a tuning parameter for several reentrant transitions between ergodic and weak ergodicity breaking regimes. The former regime shows rapid thermalization of correlation functions and absence of scars in the Floquet spectrum of the system. The latter regime, in contrast, has scars; they lead to long-time coherent dynamics of correlation functions. We provide an analytical explanation of the existence of these regimes by going beyond a high-frequency Magnus expansion and using a novel perturbative approach valid at large drive amplitudes to derive a Floquet Hamiltonian which qualitatively explains the behavior of the driven system at arbitrary frequencies. We also discuss experiments involving finite Rydberg chains which can validate our theory. Our results demonstrate the possibility of drive-frequency-induced tuning between ergodic and weak ergodicity breaking dynamics in a disorder-free quantum many-body system.
We investigate the emergence of a scarred discrete time crystal (SDTC) phase in a periodically driven dimerized spin chain. While generic interacting Floquet systems are expected to thermalize according to the eigenstate thermalization hypothesis (ETH), we demonstrate that this system hosts quantum many-body scars (QMBS) that induce a regime of weak ergodicity breaking. Through an analysis of Floquet level statistics, entanglement entropy, and eigenstate fidelity, we identify a manifold of low-entanglement states characterized by semi-Poisson statistics embedded within an otherwise thermal spectrum. These scarred states support robust subharmonic oscillations with period doubling, signaling the spontaneous breaking of discrete time-translation symmetry. We show that the SDTC response is robust against a variety of initial state configurations, demonstrating its stability beyond fine-tuned conditions. A finite-size scaling analysis reveals that the time-crystalline lifetime grows with system size within the range accessible to our exact-diagonalization calculations. However, drawing on the general phenomenology of approximate many-body scars, we expect that hybridization between Floquet scars and the thermal continuum will eventually curtail this growth, causing the lifetime to saturate at system sizes beyond our current numerical reach. This characterizes the SDTC as a long-lived metastable dynamical regime rather than a strictly stable thermodynamic phase, providing a comprehensive framework for understanding the interplay between periodic driving and constrained many-body dynamics in disorder-free systems.
Quantum scars are special eigenstates of many-body systems that evade thermalization. They were first discovered in the PXP model, a well-known effective description of Rydberg atom arrays. Despite significant theoretical efforts, the fundamental origin of PXP scars remains elusive. By investigating the discretized dynamics of the PXP model as a function of the Trotter step τ, we uncover a remarkable correspondence between the zero- and two-particle eigenstates of the integrable Floquet-PXP cellular automaton at τ=π/2 and the PXP many-body scars of the time-continuous limit. Specifically, we demonstrate that PXP scars are adiabatically connected to the eigenstates of the τ=π/2 Floquet operator. Building on this result, we propose a protocol for achieving high-fidelity preparation of PXP scars in Rydberg atom experiments.
A recent experiment in the Rydberg atom chain observed unusual oscillatory quench dynamics with a charge density wave initial state, and theoretical works identified a set of many-body "scar states" showing nonthermal behavior in the Hamiltonian as potentially responsible for the atypical dynamics. In the same nonintegrable Hamiltonian, we discover several eigenstates at an infinite temperature that can be represented exactly as matrix product states with a finite bond dimension, for both periodic boundary conditions (two exact E=0 states) and open boundary conditions (two E=0 states and one each E=±sqrt[2]). This discovery explicitly demonstrates the violation of the strong eigenstate thermalization hypothesis in this model and uncovers exact quantum many-body scar states. These states show signatures of translational symmetry breaking with a period-2 bond-centered pattern, despite being in one dimension at an infinite temperature. We show that the nearby many-body scar states can be well approximated as "quasiparticle excitations" on top of our exact E=0 scar states and propose a quasiparticle explanation of the strong oscillations observed in experiments.
We study the dynamics of a periodically driven Rydberg chain starting from the state with zero Rydberg excitations (vacuum state denoted by $|0\ensuremath{\rangle}$) using a square pulse protocol in the high drive amplitude limit. We show, using exact diagonalization for finite system sizes $(L\ensuremath{\le}26)$, that the Floquet Hamiltonian of the system, within a range of drive frequencies that we chart out, hosts a set of quantum scars that have large overlap with the $|0\ensuremath{\rangle}$ state. These scars are distinct from their counterparts having high overlap with the maximal Rydberg excitation state $(|{\mathbb{Z}}_{2}\ensuremath{\rangle})$; they coexist with the latter class of scars and lead to persistent coherent oscillations of the density-density correlator starting from the $|0\ensuremath{\rangle}$ state. We also identify special drive frequencies at which the system undergoes perfect dynamic freezing, and we provide an analytic explanation for this phenomenon. Finally, we demonstrate that for a wide range of drive frequencies, the system reaches a steady state with subthermal values of the density-density correlator. The presence of such subthermal steady states, which are absent for dynamics starting from the $|{\mathbb{Z}}_{2}\ensuremath{\rangle}$ state, imply a weak violation of the eigenstate thermalization hypothesis in finite-sized Rydberg chains distinct from that due to the scar-induced persistent oscillations reported earlier. We conjecture that in the thermodynamic limit, such states may exist as prethermal steady states that show anomalously slow relaxation. We supplement our numerical results by deriving an analytic expression for the Floquet Hamiltonian using a Floquet perturbation theory in the high amplitude limit, which provides an analytic, albeit qualitative, understanding of these phenomena at arbitrary drive frequencies. We discuss experiments that can test our theory.