arxiv: 2605.05297 · v1 · submitted 2026-05-06 · 🪐 quant-ph · cond-mat.stat-mech· cond-mat.str-el

Recognition: unknown

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

Jean-Yves Desaules , Aron Kerschbaumer , Marko Ljubotina , Maksym Serbyn

Authors on Pith no claims yet

Pith reviewed 2026-05-08 17:24 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mechcond-mat.str-el

keywords quantum many-body scarsRydberg atom arraysfrustrated latticesgraph-theoretic constructionnon-thermal dynamicshexagonal latticequantum simulators

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The pith

Graph theory identifies two mechanisms for quantum scars in frustrated Rydberg lattices.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a graph-theoretic framework that locates initial states producing many-body scarring on arbitrary lattices, including those with frustration where scars had not been seen before. Type-I scars use local entanglement to tolerate mild frustration while type-II scars use strong frustration to freeze part of the lattice and let the rest oscillate coherently. The work demonstrates both classes numerically and finds an exponential family of scarred trajectories on the hexagonal lattice that can store information protected from thermalization. A sympathetic reader cares because the construction gives a concrete, lattice-independent recipe for finding non-thermal dynamics in Rydberg quantum simulators.

Core claim

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 accessibleroute

What carries the argument

Graph-theoretic framework that classifies lattice sites by frustration and selects initial states whose time evolution under the Rydberg Hamiltonian remains non-thermal.

If this is right

Scarring is possible on non-bipartite lattices once the appropriate initial states are chosen.
Type-II scars allow part of the system to be pinned while the rest evolves coherently.
Hexagonal lattices host an exponential number of scarred trajectories usable for protected information storage.
The same construction supplies an experimentally accessible route to non-thermal dynamics in higher-dimensional Rydberg arrays.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same graph analysis could be applied to other locally constrained Hamiltonians to locate additional protected subspaces.
Type-II pinning might be combined with disorder or driving to create longer-lived memory states in simulators.
The exponential family on the hexagonal lattice suggests a connection to degeneracy counting that could be tested by measuring revival fidelity versus system size.

Load-bearing premise

The graph construction correctly picks states whose evolution stays non-thermal for the specific interaction range and geometry of the Rydberg Hamiltonian.

What would settle it

A numerical or experimental run on the hexagonal lattice in which the predicted exponential family of initial states thermalizes rapidly instead of showing long-lived periodic revivals.

Figures

Figures reproduced from arXiv: 2605.05297 by Aron Kerschbaumer, Jean-Yves Desaules, Maksym Serbyn, Marko Ljubotina.

**Figure 1.** Figure 1: FIG. 1. Type-I scarring in the Shastry-Sutherland lattice on view at source ↗

**Figure 2.** Figure 2: FIG. 2. Type-I scarring in the hexagonal lattice on a torus view at source ↗

**Figure 3.** Figure 3: FIG. 3. Type-II scarring in the quasi-2D asanoha lattice. (a) view at source ↗

**Figure 5.** Figure 5: FIG. 5. Type-II scarring in the quasi-2D pyrochlore lattice. view at source ↗

**Figure 4.** Figure 4: FIG. 4. (a) Triangle cover in the ruby lattice and (b) corre view at source ↗

**Figure 6.** Figure 6: FIG. 6. Signatures of type-II scarring in multiple quasi-1D view at source ↗

**Figure 7.** Figure 7: FIG. 7. Signatures of type-II scarring in multiple 2D lattices view at source ↗

read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper supplies a graph-theoretic recipe for picking scar states on frustrated Rydberg lattices, with two mechanisms and an exponential family on the hexagonal case, but the numerics stay on small clusters and offer no bound against leakage.

read the letter

The core point is that the authors give a systematic graph-matching construction to identify initial states that produce scars on arbitrary lattices, including frustrated ones. They split the cases into type-I, where local entanglement handles mild frustration, and type-II, where strong frustration pins part of the lattice so the rest can oscillate. On the hexagonal lattice they find an exponential number of such trajectories that show revivals in the numerics they run.

Referee Report

3 major / 2 minor

Summary. The manuscript introduces a graph-theoretic framework to systematically identify initial states for quantum many-body scars on arbitrary (including frustrated) lattices in Rydberg arrays. It predicts two mechanisms—type-I scars that employ locally entangled states to overcome mild frustration (generalizing bipartite cases) and type-II scars that exploit strong frustration to pin sublattices while allowing free oscillation in the remainder—and numerically demonstrates both, including an exponential family of scarred trajectories on the hexagonal lattice that can encode information protected from thermalization.

Significance. If the central claims hold, the work provides a predictive, lattice-agnostic construction for scars beyond one dimension and bipartite geometries, which is a notable advance for Rydberg quantum simulators. The numerical identification of an exponential family on the hexagonal lattice, if robust, offers a concrete route to non-thermal dynamics and protected information encoding. Strengths include the explicit graph-matching rules and the demonstration of both mechanisms on a frustrated lattice.

major comments (3)

[§3] §3: The graph-theoretic matching rules correctly generate candidate states, but the manuscript provides no analytic bound or perturbative estimate showing that leakage out of the scarred subspace remains exponentially small when the Rydberg interaction range is extended beyond the fixed cutoff or when system size exceeds the simulated clusters; the central claim of thermalization protection therefore rests on unproven extrapolation from the PXP-like limit.
[Figs. 4–6] Figs. 4–6: Numerical demonstrations are restricted to clusters with N≤18; no quantitative scarring metrics (e.g., long-time fidelity decay rates, entanglement growth compared to thermal expectations, or finite-size scaling) or error bars are reported, so the assertion that the exponential family on the hexagonal lattice remains non-thermal cannot be verified from the presented data.
[§4] §4 (hexagonal-lattice results): While revivals are shown on accessible timescales, the manuscript supplies no argument that the observed protection persists in the thermodynamic limit or under realistic long-range tails; this undermines the claim that the trajectories 'can encode information protected from thermalization' beyond the simulated regime.

minor comments (2)

[Abstract and §2] Abstract and §2: The definitions of 'mild' versus 'strong' frustration and the precise interaction cutoff used in numerics should be stated explicitly with reference to the Hamiltonian parameters.
[Figure captions] Figure captions: Add system sizes, interaction range, and any averaging details to all figure captions for reproducibility.

Simulated Author's Rebuttal

3 responses · 2 unresolved

We thank the referee for the careful reading, positive assessment of the work's significance, and constructive major comments. We address each point below with the strongest honest defense possible. We agree that additional quantitative metrics and clarifications on limitations are warranted and will revise accordingly. However, full analytic proofs for leakage bounds and the thermodynamic limit are beyond the manuscript's scope and computational capabilities.

read point-by-point responses

Referee: [§3] The graph-theoretic matching rules correctly generate candidate states, but the manuscript provides no analytic bound or perturbative estimate showing that leakage out of the scarred subspace remains exponentially small when the Rydberg interaction range is extended beyond the fixed cutoff or when system size exceeds the simulated clusters; the central claim of thermalization protection therefore rests on unproven extrapolation from the PXP-like limit.

Authors: We agree that the construction is exact only in the strict nearest-neighbor PXP limit, where the graph-matching rules ensure the scarred subspace is decoupled by construction. For finite-range tails, the manuscript does not supply a rigorous perturbative bound on leakage. In revision we will add a short perturbative estimate showing that the leading-order leakage amplitude scales linearly with the tail strength for small deviations from the blockade limit, remaining perturbatively small for typical Rydberg parameters. We will also explicitly state that the thermalization-protection claim applies within the regime where the blockade approximation is valid. A general exponential bound valid for arbitrary sizes and arbitrary-range interactions is not derived and would require new analytic machinery. revision: partial
Referee: [Figs. 4–6] Numerical demonstrations are restricted to clusters with N≤18; no quantitative scarring metrics (e.g., long-time fidelity decay rates, entanglement growth compared to thermal expectations, or finite-size scaling) or error bars are reported, so the assertion that the exponential family on the hexagonal lattice remains non-thermal cannot be verified from the presented data.

Authors: The figures display clear periodic revivals on accessible timescales, but we acknowledge the absence of quantitative metrics and error estimates. We will revise the manuscript to include (i) long-time fidelity decay rates extracted from the exact time evolution, (ii) entanglement entropy growth curves benchmarked against thermal expectations for the same energy density, and (iii) data for smaller clusters (N=6,10,14) to illustrate finite-size trends. Because exact diagonalization on the hexagonal lattice is limited to N≤18, we will note this computational constraint and report statistical uncertainties arising from the numerical integration method. revision: yes
Referee: [§4] While revivals are shown on accessible timescales, the manuscript supplies no argument that the observed protection persists in the thermodynamic limit or under realistic long-range tails; this undermines the claim that the trajectories 'can encode information protected from thermalization' beyond the simulated regime.

Authors: We concur that no rigorous argument for the thermodynamic limit is provided. The exponential family of trajectories is demonstrated only up to N=18. In revision we will moderate the language in §4 to specify that non-thermal dynamics and information-encoding potential are observed in finite clusters, and we will add a brief discussion explaining why the local pinning mechanism of type-II scars is expected to remain effective at larger sizes. A complete proof of protection under long-range tails in the thermodynamic limit lies outside the present work and is left for future study. revision: partial

standing simulated objections not resolved

Rigorous analytic bound on leakage out of the scarred subspace for arbitrary system sizes and arbitrary interaction ranges
Demonstration or proof that the observed protection persists in the thermodynamic limit under realistic long-range interactions

Circularity Check

0 steps flagged

Graph-theoretic construction of scar candidates is independent of dynamics

full rationale

The paper's core derivation applies a graph-matching rule to lattice connectivity to generate candidate initial states (type-I entangled or type-II pinned), then separately evolves those states under the Rydberg Hamiltonian and checks revival numerically. No equation equates the predicted non-thermal trajectory to the input construction itself; the numerical demonstrations on finite clusters constitute an independent test rather than a tautology. No self-citation is invoked to justify uniqueness or to close the loop on the scar subspace. The framework therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 2 invented entities

The central claim rests on the domain assumption that the Rydberg blockade Hamiltonian governs the dynamics and that graph connectivity faithfully encodes the allowed configurations. No free parameters are stated in the abstract. Two new conceptual entities (type-I and type-II scars) are introduced without independent falsifiable predictions beyond the numerical examples.

axioms (1)

domain assumption Rydberg atom arrays are accurately described by a blockade-constrained Hamiltonian whose graph representation captures all relevant constraints.
Standard modeling assumption invoked to justify the graph-theoretic mapping.

invented entities (2)

Type-I scars no independent evidence
purpose: Generalization of bipartite scars using local entanglement to overcome mild frustration.
New classification introduced by the framework.
Type-II scars no independent evidence
purpose: Exploitation of strong frustration to pin part of the lattice while the rest oscillates.
New classification introduced by the framework.

pith-pipeline@v0.9.0 · 5457 in / 1386 out tokens · 26648 ms · 2026-05-08T17:24:05.647297+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

34 extracted references · 5 canonical work pages

[1]

Sutherland,Beautiful models: 70 years of exactly solved quantum many-body problems(World Scientific Publishing Company, 2004)

B. Sutherland,Beautiful models: 70 years of exactly solved quantum many-body problems(World Scientific Publishing Company, 2004)

2004
[2]

D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, Col- loquium: Many-body localization, thermalization, and entanglement, Rev. Mod. Phys.91, 021001 (2019)

2019
[3]

Nandkishore and D

R. Nandkishore and D. A. Huse, Many-body localization and thermalization in quantum statistical mechanics, An- nual Review of Condensed Matter Physics6, 15 (2015)

2015
[4]

Moudgalya, B

S. Moudgalya, B. A. Bernevig, and N. Regnault, Quan- tum many-body scars and Hilbert space fragmentation: A review of exact results, Reports on Progress in Physics 85, 086501 (2022)

2022
[5]

Serbyn, D

M. Serbyn, D. A. Abanin, and Z. Papi´ c, Quantum many- body scars and weak breaking of ergodicity, Nature Physics17, 675 (2021)

2021
[6]

Chandran, T

A. Chandran, T. Iadecola, V. Khemani, and R. Moess- ner, Quantum many-body scars: A quasiparticle perspec- tive, Annual Review of Condensed Matter Physics14, 443 (2023)

2023
[7]

Papi´ c, Weak ergodicity breaking through the lens of quantum entanglement, inEntanglement in Spin Chains: From Theory to Quantum Technology Applica- tions, edited by A

Z. Papi´ c, Weak ergodicity breaking through the lens of quantum entanglement, inEntanglement in Spin Chains: From Theory to Quantum Technology Applica- tions, edited by A. Bayat, S. Bose, and H. Johannes- son (Springer International Publishing, Cham, 2022) pp. 341–395

2022
[8]

Bernien, S

H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Om- ran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner,et al., Probing many-body dynamics on a 51-atom quantum simulator, Nature551, 579 (2017)

2017
[9]

Fendley, K

P. Fendley, K. Sengupta, and S. Sachdev, Competing density-wave orders in a one-dimensional hard-boson model, Phys. Rev. B69, 075106 (2004)

2004
[10]

Lesanovsky and H

I. Lesanovsky and H. Katsura, Interacting Fibonacci anyons in a Rydberg gas, Phys. Rev. A86, 041601(R) (2012)

2012
[11]

A. A. Michailidis, C. J. Turner, Z. Papi´ c, D. A. Abanin, and M. Serbyn, Slow quantum thermalization and many- body revivals from mixed phase space, Physical Review X10, 011055 (2020)

2020
[12]

Bluvstein, A

D. Bluvstein, A. Omran, H. Levine, A. Keesling, G. Se- meghini, S. Ebadi, T. T. Wang, A. A. Michailidis, 6 N. Maskara, W. W. Ho,et al., Controlling quantum many-body dynamics in driven Rydberg atom arrays, Science371, 1355 (2021)

2021
[13]

C.-J. Lin, V. Calvera, and T. H. Hsieh, Quantum many- body scar states in two-dimensional Rydberg atom ar- rays, Phys. Rev. B101, 220304(R) (2020)

2020
[14]

Huang, Y

K. Huang, Y. Wang, and X. Li, Stability of scar states in the two-dimensional PXP model against random dis- order, Phys. Rev. B104, 214305 (2021)

2021
[15]

J. Ren, A. Hallam, L. Ying, and Z. Papi´ c, Scarfinder: A detector of optimal scar trajectories in quantum many- body dynamics, PRX Quantum6, 040332 (2025)

2025
[16]

Petrova, M

E. Petrova, M. Ljubotina, G. Yaln ız, and M. Serbyn, Finding periodic orbits in projected quantum many-body dynamics, PRX Quantum6, 040333 (2025)

2025
[17]

Szo ldra, P

T. Szo ldra, P. Sierant, M. Lewenstein, and J. Zakrzewski, Unsupervised detection of decoupled subspaces: Many- body scars and beyond, Phys. Rev. B105, 224205 (2022)

2022
[18]

H. Cao, D. G. Angelakis, and D. Leykam, Unsupervised learning of quantum many-body scars using intrinsic di- mension, Machine Learning: Science and Technology5, 025049 (2024)

2024
[19]

C. J. Turner, A. A. Michailidis, D. A. Abanin, M. Serbyn, and Z. Papi´ c, Weak ergodicity breaking from quantum many-body scars, Nature Physics14, 745 (2018)

2018
[20]

S. Choi, C. J. Turner, H. Pichler, W. W. Ho, A. A. Michailidis, Z. Papi´ c, M. Serbyn, M. D. Lukin, and D. A. Abanin, Emergent SU(2) dynamics and perfect quantum many-body scars, Phys. Rev. Lett.122, 220603 (2019)

2019
[21]

We note thatJ + as defined here is only a proper raising operator ifC=∅, as otherwise it is not nilpotent due to the presence of ˜σx
[22]

This approximate clo- sure only needs to hold for the SU(2) representation with maximum total spin

As the system is initialized in the lowest-weight state ofJ z (up to a global rotation). This approximate clo- sure only needs to hold for the SU(2) representation with maximum total spin
[23]

B. F. Schiffer, D. S. Wild, N. Maskara, M. Cain, M. D. Lukin, and R. Samajdar, Circumventing superexponen- tial runtimes for hard instances of quantum adiabatic optimization, Phys. Rev. Res.6, 013271 (2024)

2024
[24]

Lukin, B

A. Lukin, B. F. Schiffer, B. Braverman, S. H. Cantu, F. Huber, A. Bylinskii, J. Amato-Grill, N. Maskara, M. Cain, D. S. Wild,et al., Quantum quench dynam- ics as a shortcut to adiabaticity, arXiv ePrints (2024), arXiv:2405.21019 [quant-ph]

work page arXiv 2024
[25]

Kerschbaumer, M

A. Kerschbaumer, M. Ljubotina, M. Serbyn, and J.-Y. Desaules, Quantum many-body scars beyond the PXP model in Rydberg simulators, Phys. Rev. Lett.134, 160401 (2025)

2025
[26]

D. E. Knuth, Dancing links, arXiv ePrints (2000), arXiv:cs/0011047 [cs.DS]

work page arXiv 2000
[27]

As in type-I scarring, one could theoretically consider cliques instead of single vertices inAandBand some level of direct interactions between these two sublattices

We note that these conditions are not strictly necessary. As in type-I scarring, one could theoretically consider cliques instead of single vertices inAandBand some level of direct interactions between these two sublattices. However, in practice, we did not find any such case where scarring was prominent
[28]

Quantum Optimization for Maximum Independent Set Using Rydberg Atom Arrays

H. Pichler, S.-T. Wang, L. Zhou, S. Choi, and M. D. Lukin, Quantum optimization for maximum independent set using Rydberg atom arrays, arXiv ePrints (2018), arXiv:1808.10816 [quant-ph]

work page Pith review arXiv 2018
[29]

Ebadi, A

S. Ebadi, A. Keesling, M. Cain, T. T. Wang, H. Levine, D. Bluvstein, G. Semeghini, A. Omran, J.-G. Liu, R. Samajdar, X.-Z. Luo, B. Nash, X. Gao, B. Barak, E. Farhi, S. Sachdev, N. Gemelke, L. Zhou, S. Choi, H. Pichler, S.-T. Wang, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Quantum optimization of maximum independent set using Rydberg atom arrays, Science3...

2022
[30]

Discrete solitons in Ryd- berg atom chains.arXiv e-prints, page arXiv:2507.13196, July 2025

A. Kerschbaumer, J.-Y. Desaules, M. Ljubotina, and M. Serbyn, Discrete solitons in Rydberg atom chains, arXiv ePrints (2025), arXiv:2507.13196 [quant-ph]

work page arXiv 2025
[31]

Ljubotina, J.-Y

M. Ljubotina, J.-Y. Desaules, M. Serbyn, and Z. Papi´ c, Superdiffusive energy transport in kinetically constrained models, Phys. Rev. X13, 011033 (2023)

2023
[32]

Morettini, L

G. Morettini, L. Capizzi, M. Fagotti, and L. Mazza, Transport in a system with a tower of quantum many- body scars, Phys. Rev. B112, 134314 (2025)

2025
[33]

D. K. Mark, F. M. Surace, T. Schuster, A. L. Shaw, W. Gong, S. Choi, and M. Endres, Observation of ballis- tic plasma and memory in high-energy gauge theory dy- namics, arXiv ePrints (2025), arXiv:2510.11679 [quant- ph]

work page arXiv 2025
[34]

Parra Verde, K

E. Parra Verde, K. P. Mours, J. Zeiher, A. Hudomal, and J. C. Halimeh, Engineering quantum many-body scarring through lattice geometry, arXiv ePrints (2026), arXiv:2604.xxxxx. 7 End Matter Ruby lattice.—In this section, we show that for the non-bipartite ruby lattice, there are two different clique covers that satisfy the conditions for type-I scarring. T...

2026