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arXiv:2003.04516 · Physical review. B./Physical review. B

Quantum many-body scar states in two-dimensional Rydberg atom arrays

Cheng-Ju Lin, Vladimir Calvera, Timothy H. Hsieh

Published Jun 22, 2020• 105 citations
arXivHTMLPDF

Abstract

We find exponentially many exact quantum many-body scar states in a two-dimensional PXP model---an effective model for a two-dimensional Rydberg atom array in the nearest-neighbor blockade regime. Such scar states are remarkably simple valence bond solids despite being at an effectively infinite temperature, and thus strongly violate the eigenstate thermalization hypothesis. For a particular boundary condition, such eigenstates have integer-valued energies. Moreover, certain charge-density-wave initial states give rise to strong oscillations in the Rydberg excitation density after a quantum quench and towerlike structures in their overlaps with eigenstates.

DOI
10.1103/physrevb.101.220304

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We find exponentially many exact quantum many-body scar states in a two-dimensional PXP model---an effective model for a two-dimensional Rydberg atom array in the nearest-neighbor blockade regime. Such scar states are remarkably simple valence bond solids despite being at an effectively infinite temperature, and thus strongly violate the eigenstate thermalization hypothesis. For a particular boundary condition, such eigenstates have integer-valued energies. Moreover, certain charge-density-wave initial states give rise to strong oscillations in the Rydberg excitation density after a quantum quench and towerlike structures in their overlaps with eigenstates.
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.
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.
Quantum scars are nonthermal eigenstates characterized by low entanglement entropy, initially detected in systems subject to nearest-neighbor Rydberg blockade, the so-called PXP model. While most of these special eigenstates elude an analytical description and seem to hybridize with nearby thermal eigenstates for large systems, some of them can be written as matrix product states with size-independent bond dimension. We study the response of these exact quantum scars to perturbations by analyzing the scaling of the fidelity susceptibility with system size. We find that some of them are anomalously stable at first order in perturbation theory, in sharp contrast to the eigenstate thermalization hypothesis. However, this stability seems to break down when all orders are taken into account. We further investigate models with larger blockade radius and find a set of exact quantum scars that we write down analytically and compare with the PXP exact eigenstates. We show that they exhibit the same robustness against perturbations at first order.
We study a model of Rydberg atoms in a nearest-neighbor Rydberg blockaded regime, introduced by Lesanovsky [Phys. Rev. Lett. 108, 105301 (2012)]. This many-body model (which has one parameter zzz) has an exactly known gapped liquid ground state, and two exactly known low-lying excitations. We discover two exact low-lying eigenstates. We also discuss behavior of the model at small parameter zzz and its proximity to an integrable model. Lastly, we discuss connections between the Lesanovsky model at intermediate zzz and the so-called PXP model. The PXP model describes a recent experiment that observed unusual revivals from a charge-density-wave initial state, which are attributed to a set of many-body ``scar states'' which do not obey the eigenstate thermalization hypothesis. We discuss the possibility of approximate scar states in the Lesanovsky model and present two approximations for them.
In this work, we present new, highly non-trivial area-law exact zero-energy eigenstates of the one-dimensional (1D) PXP and related models. We formulate sufficient conditions for a matrix product state to represent an exact zero-energy eigenstate of a given 1D kinetically constrained model and use them to prove our new states. We also demonstrate that all previously known exact eigenstates of PXP-type models satisfy these conditions, and, in fact, can be directly deduced from them. We discuss and demonstrate a remarkably effective general numerical technique for discovering finite-bond-dimension eigenstates residing in degenerate subspaces of a broad class of Hamiltonians. Our results highlight a previously unrecognized structure characteristic of the exponentially large nullspaces in kinetically constrained models, suggesting the possibly of extensively many increasingly complex area-law zero-energy eigenstates in the thermodynamic limit. The important implications of these emergent exact eigenstates for the general thermalization phenomenology are exemplified by one of the states introduced in this work, which we propose is a member of the primary Z2\mathbb{Z}_2Z2​ quantum many-body scar tower responsible for long-lived revivals in the Rydberg atom chain experiment.
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.