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arXiv:2112.07754 · Physical Review Letters

Squeezing Quantum Many-Body Scars

Bennet Windt, Hannes Pichler

Published Mar 4, 2022• 23 citations
arXivHTMLPDF

Abstract

We develop an analytical approach for the description of quantum many-body scars in PXP models. We show that the scarred dynamics in the PXP model on a complete bipartite graph can be interpreted as a one-dimensional chiral scattering problem, and solve this problem analytically. The insights from this analysis allow us to predict that dynamical signatures of scars in PXP models can be enhanced by spin squeezing the initial states. We show numerically that this stabilization mechanism applies not only to the complete bipartite graph but also to one- and two-dimensional lattices, which are relevant for Rydberg atom array experiments. Moreover, our findings provide a physical motivation for Hamiltonian deformations reminiscent of those known to produce perfect scars.

DOI
10.1103/physrevlett.128.090606

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We develop an analytical approach for the description of quantum many-body scars in PXP models. We show that the scarred dynamics in the PXP model on a complete bipartite graph can be interpreted as a one-dimensional chiral scattering problem, and solve this problem analytically. The insights from this analysis allow us to predict that dynamical signatures of scars in PXP models can be enhanced by spin squeezing the initial states. We show numerically that this stabilization mechanism applies not only to the complete bipartite graph but also to one- and two-dimensional lattices, which are relevant for Rydberg atom array experiments. Moreover, our findings provide a physical motivation for Hamiltonian deformations reminiscent of those known to produce perfect scars.
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.
We study the nature of the ergodicity-breaking ``quantum many-body scar'' states that appear in the PXP model describing constrained Rabi oscillations. For a wide class of bipartite lattices of Rydberg atoms, we reveal that the nearly energy-equidistant tower of these states arises from the Hamiltonian's close proximity to a generalized projector-embedding form in Phys. Rev. Lett. 119, 030601 (2017), a structure common to many models hosting quantum many-body scars. We construct a non-Hermitian but strictly local extension of the PXP model hosting exact quantum scars and show how various Hermitian scar-stabilizing extensions from the literature can be naturally understood within this framework. The exact scar states are obtained analytically as large spin states of explicitly constructed pseudospins. The quasiperiodic motion ensuing from the N\'eel state is finally shown to be the projection onto the Rydberg-constrained subspace of the precession of the large pseudospin.
Quantum many-body scars in Rydberg atom arrays have thus far only been observed on bipartite lattices, leaving open the question of whether and how they survive frustration, and what the appropriate initial states are that lead to nonthermal dynamics. We introduce a graph-theoretic framework to find suitable candidates for scarring on arbitrary lattices. Our framework predicts two distinct mechanisms: type-I scars generalize the bipartite case by using locally entangled states to overcome mild frustration, while type-II scars exploit strong frustration to pin part of the lattice, leaving the remainder to oscillate freely. We numerically demonstrate both mechanisms and uncover an exponential family of scarred trajectories on the hexagonal lattice that can encode information protected from thermalization. Our results establish scarring as a generic feature of Rydberg systems beyond one dimension and provide an experimentally accessible route to systematically probing non-thermal dynamics in quantum simulators.
Abstract We investigated the stability of quantum many-body scars under perturbations using a PXP model. Using numerical simulations, we analyzed the fidelity and correlation functions of the system to track its evolution and assess the persistence of revivals. We explored two distinct types of perturbations: imperfections in the initial state, which naturally arise in experimental settings, and disorder in the Hamiltonian, which was introduced as a computational tool to probe the system’s response to external disturbances. We found that while certain initial state modifications can partially stabilize oscillations by restricting the system’s accessible dynamics, others accelerate thermalization by increasing overlap with the full eigenstate spectrum. Similarly, disorder in the Hamiltonian gradually suppresses revivals and enhances thermalization, but scars demonstrate robustness for small perturbations. Our results provide insights into the conditions under which quantum many-body scars persist, offering valuable implications for experimental realizations and controlled quantum dynamics.
Following the recent observation of wave function revivals in large Rydberg atom quantum simulators, much effort has focused on understanding the emergence of many-body scars in nonintegrable quantum systems. Here we explore the origin of scarred wave function revivals in a family of models obtained by deforming the graph adjacency matrix of the PXP model---the effective model of Rydberg atoms in the strong Rydberg blockade regime. We consider deformations that either enhance the Rydberg constraint, ultimately resulting in an effective tight-binding model of two hypercubes joined at a single vertex, or relax the constraint until reaching the free spin-1/2 model. In the former case, we argue that the model of two joined hypercubes captures the essential features of many-body scarring present in the PXP model. On the other hand, relaxing the constraint leads to a sequence of new scarred models, some with more robust scarring signatures than the PXP model, as can be understood from the graph-theoretic viewpoint. Our results shed light on the nature of scarring in the PXP model by identifying its simple parent model, while also highlighting its distinction from the free-spin precession.
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.