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Stabilizing two-dimensional quantum scars by deformation and synchronization

Michailidis, AA, Turner, CJ, Zlatko Papić, Abanin, DA, Maksym Serbyn

Published Jun 22, 2020• 70 citations
OpenAlex

Abstract

Relaxation to a thermal state is the inevitable fate of non-equilibrium interacting quantum systems without special conservation laws. While thermalization in one-dimensional (1D) systems can often be suppressed by integrability mechanisms, in two spatial dimensions thermalization is expected to be far more effective due to the increased phase space. In this work we propose a general framework for escaping or delaying the emergence of the thermal state in two-dimensional (2D) arrays of Rydberg atoms via the mechanism of quantum scars, i.e. initial states that fail to thermalize. The suppression of thermalization is achieved in two complementary ways: by adding local perturbations or by adjusting the driving Rabi frequency according to the local connectivity of the lattice. We demonstrate that these mechanisms allow to realize robust quantum scars in various two-dimensional lattices, including decorated lattices with non-constant connectivity. In particular, we show that a small decrease of the Rabi frequency at the corners of the lattice is crucial for mitigating the strong boundary effects in two-dimensional systems. Our results identify synchronization as an important tool for future experiments on two-dimensional quantum scars.

Related papers

Stabilizing two-dimensional quantum scars by deformation and synchronization

A. A. Michailidis, C. J. Turner, Zlatko Papić +2 more

This paper proposes different mechanisms to realize robust quantum scars in two-dimensional arrays of Rydberg atoms. The results show that a small perturbation to the system can lead to a significant suppression of the thermalization rate of a small set of states

arXiv:2003.02825•Physical Review Research•Jun 22, 2020•71 citations

Systematic construction of quantum many-body scars in frustrated Rydberg arrays

Jean-Yves Desaules, Aron Kerschbaumer, Marko Ljubotina +1 more

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.

quant-pharXiv:2605.05297•May 8, 2026•0 citations

Engineering Quantum Many-Body Scars through Lattice Geometry

Erick Parra Verde, Kevin P. Mours, Johannes Zeiher +2 more

Quantum many-body scars enable persistent non-ergodic dynamics in otherwise thermalizing systems, yet their stabilization typically relies on fine-tuned initial states or engineered Hamiltonian perturbations. Here we show that lattice geometry alone can serve as a powerful and experimentally accessible control knob for inducing and enhancing scarring. By transforming a one-dimensional chain into a quasi-one-dimensional triangle-decorated lattice, we find that the fully polarized state -- normally thermalizing in the PXP model -- exhibits pronounced fidelity revivals, slow entanglement growth, and strong overlap with a tower of weakly entangled eigenstates. We trace this behavior to a geometry-induced restructuring of the constrained Hilbert space, whereby the adjacency graph decomposes into hypercube subgraphs that enforce coherent population transfer and stabilize an emergent approximate $\mathrm{su}(2)$ algebra. We propose a direct implementation in programmable arrays of tweezer-trapped Rydberg atoms, where the triangle-decorated geometry can be realized using spatial light modulators and the resulting scarring dynamics probed via time-resolved measurements of excitation density. Our results establish lattice connectivity as a design principle for engineering non-ergodic dynamics in constrained quantum systems.

cond-mat.quant-gasCross-listedarXiv:2605.05296•May 8, 2026•0 citations

Thermalization in one-dimensional quantum many-body systems

Gianluca Morettini

Thermalization in quantum many-body systems is a central problem of quantum mechanics. Despite the unitary nature of quantum evolution, isolated many-body systems often appear to relax toward states that are locally described by statistical ensembles. However, phenomena such as integrability and quantum many-body scars demonstrate that thermalization is not universal and can fail in unexpected ways, leading to nonergodic dynamics and long-lived nonequilibrium behavior. In this thesis, the problem is addressed from multiple complementary perspectives, including thermalization, integrability breaking, constrained dynamics, and quantum many-body scars, together with the development of new tensor-network methods for nonequilibrium quantum systems and quantum metrological applications. First, we study energy-filtering protocols for the preparation of thermal states, analyzing the possibility of simulating them classically through the behavior of entanglement and correlations. The effects of weak integrability breaking are then investigated in models relevant to Rydberg-atom experiments, leading to the identification of novel scattering mechanisms and the introduction of subsystem variance as a sensitive probe of weak integrability breaking. A part of the thesis is devoted to quantum many-body scars and their consequences for relaxation and transport phenomena. Their dynamical signatures are studied in both closed and open quantum systems, revealing new mechanisms that sustain long-lived nonequilibrium behavior. The thermalization processes arising during the quasi-adiabatic preparation of the ground state in the trapped Bose-Hubbard model are also examined, showing how transport constraints can stabilize low-entropy states under experimentally realistic conditions. Finally, a novel tensor-network approach based on Tree Tensor Operators is introduced for the efficient computation of the Quantum Fisher Information of generic mixed states. Applicable to both closed and open quantum systems, the method provides a promising numerical tool for quantum sensing and metrological applications.

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D. Bluvstein, A. Omran, H. Levine +12 more

The control of nonequilibrium quantum dynamics in many-body systems is challenging because interactions typically lead to thermalization and a chaotic spreading throughout Hilbert space. We investigate nonequilibrium dynamics after rapid quenches in a many-body system composed of 3 to 200 strongly interacting qubits in one and two spatial dimensions. Using a programmable quantum simulator based on Rydberg atom arrays, we show that coherent revivals associated with so-called quantum many-body scars can be stabilized by periodic driving, which generates a robust subharmonic response akin to discrete time-crystalline order. We map Hilbert space dynamics, geometry dependence, phase diagrams, and system-size dependence of this emergent phenomenon, demonstrating new ways to steer complex dynamics in many-body systems and enabling potential applications in quantum information science.

arXiv:2012.12276•Science•Feb 25, 2021•416 citations

Stability of quantum many-body scars on PXP model

Alessandra Chioquetta, Raphael C. Drumond

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.

Physica Scripta•May 19, 2025•2 citations
Relaxation to a thermal state is the inevitable fate of non-equilibrium interacting quantum systems without special conservation laws. While thermalization in one-dimensional (1D) systems can often be suppressed by integrability mechanisms, in two spatial dimensions thermalization is expected to be far more effective due to the increased phase space. In this work we propose a general framework for escaping or delaying the emergence of the thermal state in two-dimensional (2D) arrays of Rydberg atoms via the mechanism of quantum scars, i.e. initial states that fail to thermalize. The suppression of thermalization is achieved in two complementary ways: by adding local perturbations or by adjusting the driving Rabi frequency according to the local connectivity of the lattice. We demonstrate that these mechanisms allow to realize robust quantum scars in various two-dimensional lattices, including decorated lattices with non-constant connectivity. In particular, we show that a small decrease of the Rabi frequency at the corners of the lattice is crucial for mitigating the strong boundary effects in two-dimensional systems. Our results identify synchronization as an important tool for future experiments on two-dimensional quantum scars.
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.
Quantum many-body scars enable persistent non-ergodic dynamics in otherwise thermalizing systems, yet their stabilization typically relies on fine-tuned initial states or engineered Hamiltonian perturbations. Here we show that lattice geometry alone can serve as a powerful and experimentally accessible control knob for inducing and enhancing scarring. By transforming a one-dimensional chain into a quasi-one-dimensional triangle-decorated lattice, we find that the fully polarized state -- normally thermalizing in the PXP model -- exhibits pronounced fidelity revivals, slow entanglement growth, and strong overlap with a tower of weakly entangled eigenstates. We trace this behavior to a geometry-induced restructuring of the constrained Hilbert space, whereby the adjacency graph decomposes into hypercube subgraphs that enforce coherent population transfer and stabilize an emergent approximate su(2)\mathrm{su}(2)su(2) algebra. We propose a direct implementation in programmable arrays of tweezer-trapped Rydberg atoms, where the triangle-decorated geometry can be realized using spatial light modulators and the resulting scarring dynamics probed via time-resolved measurements of excitation density. Our results establish lattice connectivity as a design principle for engineering non-ergodic dynamics in constrained quantum systems.
Thermalization in quantum many-body systems is a central problem of quantum mechanics. Despite the unitary nature of quantum evolution, isolated many-body systems often appear to relax toward states that are locally described by statistical ensembles. However, phenomena such as integrability and quantum many-body scars demonstrate that thermalization is not universal and can fail in unexpected ways, leading to nonergodic dynamics and long-lived nonequilibrium behavior. In this thesis, the problem is addressed from multiple complementary perspectives, including thermalization, integrability breaking, constrained dynamics, and quantum many-body scars, together with the development of new tensor-network methods for nonequilibrium quantum systems and quantum metrological applications. First, we study energy-filtering protocols for the preparation of thermal states, analyzing the possibility of simulating them classically through the behavior of entanglement and correlations. The effects of weak integrability breaking are then investigated in models relevant to Rydberg-atom experiments, leading to the identification of novel scattering mechanisms and the introduction of subsystem variance as a sensitive probe of weak integrability breaking. A part of the thesis is devoted to quantum many-body scars and their consequences for relaxation and transport phenomena. Their dynamical signatures are studied in both closed and open quantum systems, revealing new mechanisms that sustain long-lived nonequilibrium behavior. The thermalization processes arising during the quasi-adiabatic preparation of the ground state in the trapped Bose-Hubbard model are also examined, showing how transport constraints can stabilize low-entropy states under experimentally realistic conditions. Finally, a novel tensor-network approach based on Tree Tensor Operators is introduced for the efficient computation of the Quantum Fisher Information of generic mixed states. Applicable to both closed and open quantum systems, the method provides a promising numerical tool for quantum sensing and metrological applications.
The control of nonequilibrium quantum dynamics in many-body systems is challenging because interactions typically lead to thermalization and a chaotic spreading throughout Hilbert space. We investigate nonequilibrium dynamics after rapid quenches in a many-body system composed of 3 to 200 strongly interacting qubits in one and two spatial dimensions. Using a programmable quantum simulator based on Rydberg atom arrays, we show that coherent revivals associated with so-called quantum many-body scars can be stabilized by periodic driving, which generates a robust subharmonic response akin to discrete time-crystalline order. We map Hilbert space dynamics, geometry dependence, phase diagrams, and system-size dependence of this emergent phenomenon, demonstrating new ways to steer complex dynamics in many-body systems and enabling potential applications in quantum information science.
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.