pith. sign in

arxiv: 2508.05737 · v2 · submitted 2025-08-07 · ❄️ cond-mat.quant-gas · cond-mat.str-el· physics.atom-ph· quant-ph

Quantum criticality and nonequilibrium dynamics on a Lieb lattice of Rydberg atoms

Mark R. Hirsbrunner , Milan Kornja\v{c}a , Rhine Samajdar , Siva Darbha , Majd Hamdan , Jan Balewski , Ermal Rrapaj , Sheng-Tao Wang
show 4 more authors
Daan Camps Fangli Liu Pedro L. S. Lopes Katherine Klymko
This is my paper

Pith reviewed 2026-05-19 00:11 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas cond-mat.str-elphysics.atom-phquant-ph
keywords Rydberg atomsLieb latticedensity wave orderquantum phase transitionnonequilibrium dynamicsquantum simulatorstring phasehysteresis
0
0 comments X

The pith

Rydberg atoms arranged on a Lieb lattice display multiple density-wave phases including one stabilized only by quantum fluctuations, plus a hysteretic transition and string-constrained slow dynamics.

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

The paper arranges Rydberg atoms into a Lieb lattice to explore strongly interacting quantum matter through experiments, numerics, and analytics. It maps the ground-state phase diagram and identifies several density-wave orders, one of which exists solely due to quantum fluctuations rather than classical energy minimization. Local detuning control then reveals a quantum analog of the liquid-vapor transition between two such orders, complete with hysteresis. Out-of-equilibrium quenches produce anomalously slow relaxation that matches the kinetic constraints of an emergent string phase. A reader would care because these results show how lattice geometry in neutral-atom simulators grants direct access to metastable states and constrained dynamics.

Core claim

Through a combination of quantum experiments, numerical calculations, and analytical methods on Rydberg atoms placed on the Lieb lattice, the authors map the ground states and phase diagram to identify a range of density-wave-ordered phases including a collinear phase stabilized purely by quantum fluctuations, with good agreement between theory and experiment; they then use local detuning control to discover a quantum analog of the classical liquid-vapor transition between two density-wave phases distinguished by sublattice occupation and probe its hysteretic dynamics, while out-of-equilibrium quenches reveal anomalously slow relaxation consistent with the kinetic constraints of an emergent弦

What carries the argument

The effective Rydberg Hamiltonian with blockade interactions on the Lieb lattice, which enforces nearest-neighbor exclusion and permits local detuning control to select sublattice occupations that distinguish the ordered phases.

If this is right

  • The collinear density-wave phase appears only when quantum fluctuations are included and vanishes in the classical limit.
  • Local detuning sweeps produce a first-order transition with observable hysteresis between two sublattice-distinct density waves.
  • Quench dynamics exhibit slow relaxation whose time scale is set by the kinetic constraints of the emergent string phase.
  • Geometric control of the atomic array enables programmable access to metastability and constrained thermalization in many-body systems.

Where Pith is reading between the lines

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

  • Similar lattice geometries could stabilize additional fluctuation-driven orders in other Rydberg or spin systems.
  • The observed hysteresis and slow relaxation may be harnessed to engineer long-lived metastable states for quantum information applications.
  • Extending the setup to include tunable longer-range interactions could test whether the string-phase constraints persist or give way to faster dynamics.

Load-bearing premise

The effective Rydberg Hamiltonian with blockade interactions and the assumed perfect Lieb-lattice geometry without defects or stray fields accurately capture the experimental system.

What would settle it

Repeating the density-wave mapping or the hysteretic transition measurement after introducing controlled lattice defects or stray fields that break the perfect Lieb geometry, then checking whether the reported phases and slow relaxation disappear.

Figures

Figures reproduced from arXiv: 2508.05737 by Daan Camps, Ermal Rrapaj, Fangli Liu, Jan Balewski, Katherine Klymko, Majd Hamdan, Mark R. Hirsbrunner, Milan Kornja\v{c}a, Pedro L. S. Lopes, Rhine Samajdar, Sheng-Tao Wang, Siva Darbha.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2 [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
read the original abstract

Neutral-atom quantum simulators offer a promising approach to the exploration of strongly interacting many-body systems, with applications spanning condensed matter, statistical mechanics, and high-energy physics. Through a combination of quantum experiments, numerical calculations, and analytical methods, we demonstrate a rich set of phenomena accessible on such quantum simulators by studying an array of Rydberg atoms placed on the Lieb lattice. First, we map out the ground states and phase diagram of the system, identifying a range of density-wave-ordered phases -- including a collinear phase stabilized purely by quantum fluctuations -- and find good agreement between theory and experiment. Allowing for local control of the detuning field thereafter, we discover a quantum analog of the classical liquid-vapor transition between two density-wave phases distinguished by sublattice occupation, and probe its underlying hysteretic dynamics. Furthermore, we study out-of-equilibrium quantum quenches and observe anomalously slow relaxation dynamics consistent with the kinetic constraints of an emergent string phase. These results highlight how geometric control offered by neutral-atom simulators can extend the frontiers of programmable quantum matter, enabling access to complex phases, metastability, and thermalization dynamics in many-body quantum systems.

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.

Referee Report

2 major / 2 minor

Summary. The manuscript studies an array of Rydberg atoms on the Lieb lattice using experiments, numerical calculations, and analytical methods. It maps the ground-state phase diagram, identifying multiple density-wave ordered phases including a collinear phase stabilized purely by quantum fluctuations, reports good agreement with theory, demonstrates a hysteretic quantum analog of the liquid-vapor transition between two density-wave phases, and observes slow relaxation dynamics consistent with an emergent string phase.

Significance. If the results hold, the work is significant for demonstrating the capabilities of neutral-atom quantum simulators to realize and probe complex many-body phenomena such as fluctuation-stabilized orders, metastability, and kinetically constrained dynamics on a geometrically structured lattice, thereby extending programmable quantum matter into regimes relevant to quantum criticality and nonequilibrium statistical mechanics.

major comments (2)
  1. [Experimental setup and phase-diagram mapping] The mapping of experimental site occupations and dynamics onto the theoretical phase diagram of the blockade Rydberg Hamiltonian on an ideal Lieb lattice (abstract and implied methods) is load-bearing for all headline claims, including the identification of the purely fluctuation-stabilized collinear phase and the quantum liquid-vapor transition. The manuscript provides no explicit bounds or robustness analysis on the effects of lattice defects, stray fields, or beyond-blockade interaction tails; even small perturbations could shift classical or quantum boundaries by a few percent and render the reported agreement and phase identifications inconclusive.
  2. [Out-of-equilibrium dynamics] In the nonequilibrium quench section, the attribution of anomalously slow relaxation to the kinetic constraints of an emergent string phase rests on equating observed dynamics to the ideal model. Additional simulations or controls that incorporate realistic imperfections (e.g., position disorder or detuning inhomogeneity) are needed to confirm that these effects do not produce comparable slowing, as this directly supports the central claim of string-phase-constrained thermalization.
minor comments (2)
  1. [Abstract] The abstract states 'good agreement between theory and experiment' without specifying quantitative metrics (e.g., overlap of density profiles or extracted critical points); adding these would improve clarity.
  2. Figure captions should explicitly state the system size, number of atoms, and any averaging procedures used for the experimental data shown in the phase diagram and dynamics plots.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We address the two major comments point by point below and will incorporate revisions to strengthen the presentation of robustness and controls.

read point-by-point responses

  1. Referee: [Experimental setup and phase-diagram mapping] The mapping of experimental site occupations and dynamics onto the theoretical phase diagram of the blockade Rydberg Hamiltonian on an ideal Lieb lattice (abstract and implied methods) is load-bearing for all headline claims, including the identification of the purely fluctuation-stabilized collinear phase and the quantum liquid-vapor transition. The manuscript provides no explicit bounds or robustness analysis on the effects of lattice defects, stray fields, or beyond-blockade interaction tails; even small perturbations could shift classical or quantum boundaries by a few percent and render the reported agreement and phase identifications inconclusive.

    Authors: We agree that explicit robustness checks would strengthen the mapping to the ideal model. The current manuscript emphasizes direct comparison between experiment and blockade-model numerics, which yields quantitative agreement on the locations of the density-wave phases including the fluctuation-stabilized collinear order. In the revised version we will add a dedicated appendix that quantifies the influence of measured lattice defects, residual stray fields, and van-der-Waals tails beyond the blockade radius. Using our experimental calibration data we will show that the resulting shifts in the relevant phase boundaries remain smaller than the experimental resolution and do not alter the reported phase identifications. revision: yes

  2. Referee: [Out-of-equilibrium dynamics] In the nonequilibrium quench section, the attribution of anomalously slow relaxation to the kinetic constraints of an emergent string phase rests on equating observed dynamics to the ideal model. Additional simulations or controls that incorporate realistic imperfections (e.g., position disorder or detuning inhomogeneity) are needed to confirm that these effects do not produce comparable slowing, as this directly supports the central claim of string-phase-constrained thermalization.

    Authors: We appreciate the suggestion to test the robustness of the dynamical attribution. The present analysis demonstrates that the ideal-model simulations reproduce the experimentally observed slow relaxation timescales and are consistent with the kinetic constraints of the string phase. In the revision we will include additional numerical runs that incorporate the experimentally characterized levels of position disorder and detuning inhomogeneity. These controls will show that the slowing remains negligible at the disorder strengths present in the experiment, thereby confirming that the observed dynamics are indeed dominated by the emergent string-phase constraints rather than by imperfections. revision: yes

Circularity Check

0 steps flagged

No significant circularity; central results from independent experiment-numerics comparison on standard Rydberg model

full rationale

The paper reports experimental observations of density-wave phases, a fluctuation-stabilized collinear order, a hysteretic quantum liquid-vapor transition, and slow relaxation dynamics on a Rydberg-atom Lieb lattice, cross-validated against numerical calculations and analytical methods applied to the effective blockade Hamiltonian. No load-bearing step reduces by the paper's own equations to a fitted parameter renamed as prediction, nor does any uniqueness theorem or ansatz derive from self-citation chains within this work. The mapping of site occupations and dynamics to the phase diagram uses an external, standard Rydberg model whose assumptions are stated separately from the reported data; agreement between experiment and theory functions as validation rather than tautological re-derivation. The derivation chain remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The work relies on the standard Rydberg blockade Hamiltonian and the geometric definition of the Lieb lattice taken from prior literature; no new free parameters, axioms, or invented entities are introduced in the abstract.

pith-pipeline@v0.9.0 · 5795 in / 1218 out tokens · 42005 ms · 2026-05-19T00:11:33.913242+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Phase diagram of a dual-species Rydberg atom ladder

    cond-mat.quant-gas 2026-04 unverdicted novelty 6.0

    DMRG calculations of a dual-species Rydberg atom ladder reveal Z2, Z3, Z4 ordered phases, floating phases, a smooth Z2 crossover, and a multi-critical point where Ising, chiral, and first-order lines meet.

  2. Stabilization of bulk quantum orders in finite Rydberg atom arrays

    cond-mat.quant-gas 2026-04 unverdicted novelty 6.0

    A protocol leverages the disordered phase to set unbiased boundary configurations in finite Rydberg arrays, stabilizing bulk-like quantum order in 1D and 2D simulations.

  3. Three-body interactions in Rydberg lattices

    cond-mat.quant-gas 2026-04 unverdicted novelty 6.0

    A scheme is developed to engineer strong three-body interactions in Rydberg atom lattices, allowing the effective Hamiltonian and emergent quantum phases to be modified compared to two-body-only systems.

Reference graph

Works this paper leans on

78 extracted references · 78 canonical work pages · cited by 3 Pith papers · 2 internal anchors

  1. [1]

    K. G. Wilson and M. E. Fisher, Critical Exponents in 3.99 Dimensions, Phys. Rev. Lett. 28, 240 (1972)

    work page 1972

  2. [2]

    Sachdev, Quantum Phase Transitions (Cambridge University Press, 2001)

    S. Sachdev, Quantum Phase Transitions (Cambridge University Press, 2001)

    work page 2001

  3. [3]

    Labuhn, D

    H. Labuhn, D. Barredo, S. Ravets, S. de L´ es´ eleuc, T. Macr` ı, T. Lahaye, and A. Browaeys, Tunable two- dimensional arrays of single Rydberg atoms for realizing quantum Ising models, Nature 534, 667 (2016)

    work page 2016

  4. [4]

    Bernien, S

    H. Bernien, S. Schwartz, A. Keesling, H. Levine, A. Om- ran, H. Pichler, S. Choi, A. S. Zibrov, M. Endres, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Probing many- body dynamics on a 51-atom quantum simulator, Nature 551, 579 (2017)

    work page 2017

  5. [5]

    S. J. Evered, D. Bluvstein, M. Kalinowski, S. Ebadi, T. Manovitz, H. Zhou, S. H. Li, A. A. Geim, T. T. Wang, N. Maskara, H. Levine, G. Semeghini, M. Greiner, V. Vuleti´ c, and M. D. Lukin, High-fidelity parallel entan- gling gates on a neutral-atom quantum computer, Nature 622, 268 (2023)

    work page 2023

  6. [6]

    Bluvstein, S

    D. Bluvstein, S. J. Evered, A. A. Geim, S. H. Li, H. Zhou, T. Manovitz, S. Ebadi, M. Cain, M. Kali- nowski, D. Hangleiter, J. P. Bonilla Ataides, N. Maskara, I. Cong, X. Gao, P. Sales Rodriguez, T. Karolyshyn, G. Semeghini, M. J. Gullans, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Logical quantum processor based on reconfigurable atom arrays, Nature 626, ...

    work page 2024

  7. [7]

    de L´ es´ eleuc, V

    S. de L´ es´ eleuc, V. Lienhard, P. Scholl, D. Barredo, S. We- ber, N. Lang, H. P. B¨ uchler, T. Lahaye, and A. Browaeys, Observation of a symmetry-protected topological phase of interacting bosons with rydberg atoms, Science 365, 775 (2019)

    work page 2019

  8. [8]

    Samajdar, W

    R. Samajdar, W. W. Ho, H. Pichler, M. D. Lukin, and S. Sachdev, Quantum phases of Rydberg atoms on a kagome lattice, Proc. Natl. Acad. Sci. U.S.A 118, e2015785118 (2021)

    work page 2021

  9. [9]

    Verresen, M

    R. Verresen, M. D. Lukin, and A. Vishwanath, Prediction of Toric Code Topological Order from Rydberg Blockade, Phys. Rev. X 11, 031005 (2021)

    work page 2021

  10. [10]

    Semeghini, H

    G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen, H. Pichler, M. Kali- nowski, R. Samajdar, A. Omran, S. Sachdev, A. Vish- wanath, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Prob- ing topological spin liquids on a programmable quantum simulator, Science 374, 1242 (2021)

    work page 2021

  11. [11]

    Kornjaˇ ca, R

    M. Kornjaˇ ca, R. Samajdar, T. Macr` ı, N. Gemelke, S.- T. Wang, and F. Liu, Trimer quantum spin liquid in a honeycomb array of Rydberg atoms, Commun. Phys. 6, 358 (2023)

    work page 2023

  12. [12]

    Bluvstein, A

    D. Bluvstein, A. Omran, H. Levine, A. Keesling, G. Se- meghini, S. Ebadi, T. T. Wang, A. A. Michailidis, N. Maskara, W. W. Ho, S. Choi, M. Serbyn, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Controlling quantum many- body dynamics in driven Rydberg atom arrays, Science 371, 1355 (2021)

    work page 2021

  13. [13]

    Keesling, A

    A. Keesling, A. Omran, H. Levine, H. Bernien, H. Pich- ler, S. Choi, R. Samajdar, S. Schwartz, P. Silvi, S. Sachdev, P. Zoller, M. Endres, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Quantum Kibble–Zurek mechanism and critical dynamics on a programmable Rydberg sim- ulator, Nature 568, 207 (2019)

    work page 2019

  14. [14]

    Ebadi, T

    S. Ebadi, T. T. Wang, H. Levine, A. Keesling, G. Se- meghini, A. Omran, D. Bluvstein, R. Samajdar, H. Pich- ler, W. W. Ho, S. Choi, S. Sachdev, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Quantum phases of matter 8 on a 256-atom programmable quantum simulator, Nature 595, 227 (2021)

    work page 2021

  15. [15]

    Zhang, S

    J. Zhang, S. H. Cant´ u, F. Liu, A. Bylinskii, B. Braver- man, F. Huber, J. Amato-Grill, A. Lukin, N. Gemelke, A. Keesling, S.-T. Wang, Y. Meurice, and S.-W. Tsai, Probing quantum floating phases in Rydberg atom ar- rays, Nat. Commun. 16, 712 (2025)

    work page 2025

  16. [16]

    Samajdar and D

    R. Samajdar and D. A. Huse, Quantum and classical coarsening and their interplay with the Kibble-Zurek mechanism, (2024), arXiv:2401.15144 [quant-ph]

    work page arXiv 2024

  17. [17]

    Manovitz, S

    T. Manovitz, S. H. Li, S. Ebadi, R. Samajdar, A. A. Geim, S. J. Evered, D. Bluvstein, H. Zhou, N. U. Koylu- oglu, J. Feldmeier, P. E. Dolgirev, N. Maskara, M. Kali- nowski, S. Sachdev, D. A. Huse, M. Greiner, V. Vuleti´ c, and M. D. Lukin, Quantum coarsening and collective dy- namics on a programmable simulator, Nature 638, 86–92 (2025)

    work page 2025

  18. [18]

    Darbha, M

    S. Darbha, M. Kornjaˇ ca, F. Liu, J. Balewski, M. R. Hirs- brunner, P. L. S. Lopes, S.-T. Wang, R. Van Beeumen, D. Camps, and K. Klymko, False vacuum decay and nu- cleation dynamics in neutral atom systems, Phys. Rev. B 110, 155103 (2024)

    work page 2024

  19. [19]

    Darbha, M

    S. Darbha, M. Kornjaˇ ca, F. Liu, J. Balewski, M. R. Hirs- brunner, P. L. S. Lopes, S.-T. Wang, R. Van Beeumen, K. Klymko, and D. Camps, Long-lived oscillations of metastable states in neutral atom systems, Phys. Rev. B 110, 155114 (2024)

    work page 2024

  20. [20]

    Vodeb, J.-Y

    J. Vodeb, J.-Y. Desaules, A. Hallam, A. Rava, G. Hu- mar, D. Willsch, F. Jin, M. Willsch, K. Michielsen, and Z. Papi´ c, Stirring the false vacuum via interacting quan- tized bubbles on a 5,564-qubit quantum annealer, Nat. Phys. 21, 386 (2025)

    work page 2025

  21. [21]

    Z.-H. Zhu, Y. Liu, G. Lagnese, F. M. Surace, W.-Y. Zhang, M.-G. He, J. C. Halimeh, M. Dalmonte, S. C. Morampudi, F. Wilczek, Z.-S. Yuan, and J.-W. Pan, Probing false vacuum decay on a cold-atom gauge-theory quantum simulator, (2024), arXiv:2411.12565 [cond- mat.quant-gas]

    work page arXiv 2024

  22. [22]

    F. M. Surace, A. Lerose, O. Katz, E. R. Bennewitz, A. Schuckert, D. Luo, A. De, B. Ware, W. Morong, K. Collins, C. Monroe, Z. Davoudi, and A. V. Gorshkov, String-breaking dynamics in quantum adiabatic and di- abatic processes, (2024), arXiv:2411.10652 [quant-ph]

    work page internal anchor Pith review arXiv 2024

  23. [23]

    D. Luo, F. M. Surace, A. De, A. Lerose, E. R. Bennewitz, B. Ware, A. Schuckert, Z. Davoudi, A. V. Gorshkov, O. Katz, and C. Monroe, Quantum simulation of bubble nucleation across a quantum phase transition, (2025), arXiv:2505.09607 [quant-ph]

    work page arXiv 2025

  24. [24]

    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, Phys. Rev. X 10, 011055 (2020)

    work page 2020

  25. [25]

    Fradkin, S

    E. Fradkin, S. A. Kivelson, and J. M. Tranquada, Collo- quium: Theory of intertwined orders in high temperature superconductors, Rev. Mod. Phys. 87, 457 (2015)

    work page 2015

  26. [26]

    Maffi, N

    L. Maffi, N. Tausendpfund, M. Rizzi, and M. Burrello, Quantum Simulation of the Tricritical Ising Model in Tunable Josephson Junction Ladders, Phys. Rev. Lett. 132, 226502 (2024)

    work page 2024

  27. [27]

    H. Wang, X. Li, and C. Li, Tricritical Kibble-Zurek Scal- ing in Rydberg Atom Ladders, (2025), arXiv:2505.12979 [cond-mat.quant-gas]

    work page arXiv 2025

  28. [28]

    Gould, S

    O. Gould, S. G¨ uyer, and K. Rummukainen, First-order electroweak phase transitions: A nonperturbative up- date, Phys. Rev. D 106, 114507 (2022)

    work page 2022

  29. [29]

    Samajdar, W

    R. Samajdar, W. W. Ho, H. Pichler, M. D. Lukin, and S. Sachdev, Complex Density Wave Orders and Quantum Phase Transitions in a Model of Square-Lattice Rydberg Atom Arrays, Phys. Rev. Lett. 124, 103601 (2020)

    work page 2020

  30. [30]

    Scholl, M

    P. Scholl, M. Schuler, H. J. Williams, A. A. Eberharter, D. Barredo, K.-N. Schymik, V. Lienhard, L.-P. Henry, T. C. Lang, T. Lahaye, A. M. La¨ uchli, and A. Browaeys, Quantum simulation of 2D antiferromagnets with hun- dreds of Rydberg atoms, Nature 595, 233 (2021)

    work page 2021

  31. [31]

    Aquila: Quera’s 256-qubit neutral-atom quantum computer,

    J. Wurtz, A. Bylinskii, B. Braverman, J. Amato-Grill, S. H. Cantu, F. Huber, A. Lukin, F. Liu, P. Wein- berg, J. Long, S.-T. Wang, N. Gemelke, and A. Keesling, Aquila: Quera’s 256-qubit neutral-atom quantum com- puter, (2023), arXiv:2306.11727 [quant-ph]

    work page arXiv 2023

  32. [33]

    Fishman, S

    M. Fishman, S. R. White, and E. M. Stoudenmire, Code- base release 0.3 for ITensor, SciPost Phys. Codebases , 4 (2022)

    work page 2022

  33. [34]

    Kalinowski, R

    M. Kalinowski, R. Samajdar, R. G. Melko, M. D. Lukin, S. Sachdev, and S. Choi, Bulk and boundary quantum phase transitions in a square Rydberg atom array, Phys. Rev. B 105, 174417 (2022)

    work page 2022

  34. [35]

    Miles, R

    C. Miles, R. Samajdar, S. Ebadi, T. T. Wang, H. Pich- ler, S. Sachdev, M. D. Lukin, M. Greiner, K. Q. Wein- berger, and E.-A. Kim, Machine learning discovery of new phases in programmable quantum simulator snap- shots, Phys. Rev. Res. 5, 013026 (2023)

    work page 2023

  35. [36]

    M. J. O’Rourke and G. K.-L. Chan, Entanglement in the quantum phases of an unfrustrated Rydberg atom array, Nat. Commun. 14, 5397 (2023)

    work page 2023

  36. [37]

    Yan, Y.-C

    Z. Yan, Y.-C. Wang, R. Samajdar, S. Sachdev, and Z. Y. Meng, Emergent Glassy Behavior in a Kagome Rydberg Atom Array, Phys. Rev. Lett. 130, 206501 (2023)

    work page 2023

  37. [38]

    Jaksch, J

    D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Cˆ ot´ e, and M. D. Lukin, Fast quantum gates for neutral atoms, Phys. Rev. Lett. 85, 2208 (2000)

    work page 2000

  38. [39]

    M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, Dipole blockade and quantum information processing in mesoscopic atomic ensembles, Phys. Rev. Lett. 87, 037901 (2001)

    work page 2001

  39. [40]

    Landau, On the theory of phase transitions, in Col- lected Papers of L.D

    L. Landau, On the theory of phase transitions, in Col- lected Papers of L.D. Landau , edited by D. Ter Haar (Pergamon, 1965) pp. 193–216

    work page 1965

  40. [41]

    Park and S

    K. Park and S. Sachdev, Bond-operator theory of doped antiferromagnets: From Mott insulators with bond- centered charge order to superconductors with nodal fermions, Phys. Rev. B 64, 184510 (2001)

    work page 2001

  41. [42]

    Sachdev and K

    S. Sachdev and K. Park, Ground states of quantum an- tiferromagnets in two dimensions, Ann. Phys. 298, 58 (2002)

    work page 2002

  42. [43]

    Shackleton, A

    H. Shackleton, A. Thomson, and S. Sachdev, Decon- fined criticality and a gapless Z2 spin liquid in the square-lattice antiferromagnet, Phys. Rev. B104, 045110 (2021), publisher: American Physical Society

    work page 2021

  43. [44]

    Hindmarsh, M

    M. Hindmarsh, M. L¨ uben, J. Lumma, and M. Pauly, Phase transitions in the early universe, SciPost Phys. 9 Lect. Notes , 24 (2021)

    work page 2021

  44. [45]

    Albash and D

    T. Albash and D. A. Lidar, Adiabatic quantum compu- tation, Rev. Mod. Phys. 90, 015002 (2018)

    work page 2018

  45. [46]

    Hibat-Allah, E

    M. Hibat-Allah, E. Merali, G. Torlai, R. G. Melko, and J. Carrasquilla, Recurrent neural network wave functions for Rydberg atom arrays on kagome lattice, (2024), arXiv:2405.20384 [cond-mat.quant-gas]

    work page arXiv 2024

  46. [47]

    Ritort and P

    F. Ritort and P. Sollich, Glassy dynamics of kinetically constrained models, Adv. Phys. 52, 219 (2003)

    work page 2003

  47. [48]

    Z. Lan, M. van Horssen, S. Powell, and J. P. Garra- han, Quantum Slow Relaxation and Metastability due to Dynamical Constraints, Phys. Rev. Lett. 121, 040603 (2018)

    work page 2018

  48. [49]

    Angelone, F

    A. Angelone, F. Mezzacapo, and G. Pupillo, Superglass Phase of Interaction-Blockaded Gases on a Triangular Lattice, Phys. Rev. Lett. 116, 135303 (2016)

    work page 2016

  49. [50]

    Feldmeier, F

    J. Feldmeier, F. Pollmann, and M. Knap, Emergent Glassy Dynamics in a Quantum Dimer Model, Phys. Rev. Lett. 123, 040601 (2019)

    work page 2019

  50. [51]

    Mitra, Quantum quench dynamics, Annu

    A. Mitra, Quantum quench dynamics, Annu. Rev. Con- dens. Matter Phys. 9, 245 (2018)

    work page 2018

  51. [52]

    Bintz, V

    M. Bintz, V. S. Liu, J. Hauschild, A. Khalifa, S. Chat- terjee, M. P. Zaletel, and N. Y. Yao, Dirac spin liquid in quantum dipole arrays, (2024), arXiv:2406.00098 [cond- mat.str-el]

    work page arXiv 2024

  52. [53]

    M. Tian, R. Samajdar, and B. Gadway, Engineering frus- trated Rydberg spin models by graphical Floquet modu- lation, (2025), arXiv:2505.01513 [cond-mat.quant-gas]

    work page arXiv 2025

  53. [54]

    H. J. Manetsch, G. Nomura, E. Bataille, K. H. Le- ung, X. Lv, and M. Endres, A tweezer array with 6100 highly coherent atomic qubits, (2024), arXiv:2403.12021 [quant-ph]

    work page internal anchor Pith review arXiv 2024

  54. [55]

    Papi´ c, Weak ergodicity breaking through the lens of quantum entanglement, in Entanglement 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, in Entanglement 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

    work page 2022

  55. [56]

    Moudgalya, B

    S. Moudgalya, B. A. Bernevig, and N. Regnault, Quan- tum many-body scars and Hilbert space fragmentation: a review of exact results, Rep. Prog. Phys. 85, 086501 (2022)

    work page 2022

  56. [57]

    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)

    work page 2024

  57. [58]

    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, R. Samajdar, and M. D. Lukin, Quantum quench dynamics as a shortcut to adiabaticity, (2024), arXiv:2405.21019 [quant-ph]

    work page arXiv 2024

  58. [59]

    A. J. Daley, I. Bloch, C. Kokail, S. Flannigan, N. Pearson, M. Troyer, and P. Zoller, Practical quantum advantage in quantum simulation, Nature 607, 667 (2022)

    work page 2022

  59. [60]

    Kashyap, G

    V. Kashyap, G. Styliaris, S. Mouradian, J. I. Cirac, and R. Trivedi, Accuracy guarantees and quantum advantage in analog open quantum simulation with and without noise, Phys. Rev. X 15, 021017 (2025)

    work page 2025

  60. [61]

    S. R. White, Density matrix formulation for quantum renormalization groups, Phys. Rev. Lett.69, 2863 (1992)

    work page 1992

  61. [62]

    S. R. White, Density-matrix algorithms for quantum renormalization groups, Phys. Rev. B 48, 10345 (1993)

    work page 1993

  62. [63]

    Schollw¨ ock, The density-matrix renormalization group, Rev

    U. Schollw¨ ock, The density-matrix renormalization group, Rev. Mod. Phys. 77, 259 (2005)

    work page 2005

  63. [64]

    Fishman, S

    M. Fishman, S. R. White, and E. M. Stoudenmire, The ITensor Software Library for Tensor Network Calcula- tions, SciPost Phys. Codebases , 4 (2022)

    work page 2022

  64. [65]

    S. R. White and A. L. Chernyshev, Ne´ el Order in Square and Triangular Lattice Heisenberg Models, Phys. Rev. Lett. 99, 127004 (2007)

    work page 2007

  65. [66]

    Balents, L

    L. Balents, L. Bartosch, A. Burkov, S. Sachdev, and K. Sengupta, Putting competing orders in their place near the Mott transition, Phys. Rev. B71, 144508 (2005)

    work page 2005

  66. [67]

    Binder, Finite size scaling analysis of Ising model block distribution functions, Z

    K. Binder, Finite size scaling analysis of Ising model block distribution functions, Z. Phys. B 43, 119 (1981)

    work page 1981

  67. [68]

    Hasenbusch, K

    M. Hasenbusch, K. Pinn, and S. Vinti, Critical expo- nents of the three-dimensional Ising universality class from finite-size scaling with standard and improved ac- tions, Phys. Rev. B 59, 11471 (1999)

    work page 1999

  68. [69]

    Goldenfeld, Lectures On Phase Transitions And The Renormalization Group , Frontiers in Physics (CRC Press, Boca Raton, 1992)

    N. Goldenfeld, Lectures On Phase Transitions And The Renormalization Group , Frontiers in Physics (CRC Press, Boca Raton, 1992)

    work page 1992

  69. [70]

    Pelissetto and E

    A. Pelissetto and E. Vicari, Critical phenomena and renormalization-group theory, Phys. Rep. 368, 549 (2002)

    work page 2002

  70. [71]

    N. L. Silva, M. A. Continentino, and D. G. Barci, Quan- tum corrections for the phase diagram of systems with competing order, J. Phys. Condens. Matter 30, 225402 (2018)

    work page 2018

  71. [72]

    Kornjaˇ ca and R

    M. Kornjaˇ ca and R. Flint, Signatures of spinorial order in URu2Si2: Landau-Ginzburg theory of hastatic order, (2020), arXiv:2012.08511 [cond-mat.str-el]

    work page arXiv 2020

  72. [73]

    Friedemann, W

    S. Friedemann, W. J. Duncan, M. Hirschberger, T. W. Bauer, R. K¨ uchler, A. Neubauer, M. Brando, C. Pflei- derer, and F. M. Grosche, Quantum tricritical points in NbFe2, Nat. Phys. 14, 62 (2018)

    work page 2018

  73. [74]

    Y.-Z. Wang, S. He, L. Duan, and Q.-H. Chen, Quantum tricritical point emerging in the spin-boson model with two dissipative spins in staggered biases, Phys. Rev. B 103, 205106 (2021)

    work page 2021

  74. [75]

    L. D. Landau and E. M. Lifshitz, Statistical Physics , 3rd ed., Course Of Theoretical Physics (Butterworth- Heinemann, Oxford, England, 1996)

    work page 1996

  75. [76]

    Quantum criticality and nonequilibrium dynamics on a Lieb lattice of Rydberg atoms

    S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, Optimiza- tion by simulated annealing, Science 220, 671 (1983). 10 Supplementary Information for “Quantum criticality and nonequilibrium dynamics on a Lieb lattice of Rydberg atoms” I. EXTENDED DATA (b) (c) (a) (d) (e)Experiment Theory Extended Data Figure 1. Density of Rydberg excitations from DMRG. The gro...

    work page 1983

  76. [77]

    + u12 Ψ4 1 + Ψ4 2 + v12Ψ2 1Ψ2 2 + u3Ψ4 3 + w123 Ψ2 1 + Ψ2 2 Ψ2

    work page

  77. [78]

    (20) The third-order invariant Ψ3(Ψ2 1 − Ψ2

    work page

  78. [79]

    necessarily drives the transition first-order close to the tricritical point [34, 41, 42, 71, 72]. It is possible that the disordered–star transition becomes second-order away from the intersection at larger values of Rb/a, requiring the existence of an additional tricritical point. Furthermore, the collinear–star phase transition numerically appears to b...

    work page