arxiv: 2604.24744 · v1 · submitted 2026-04-27 · ❄️ cond-mat.quant-gas · cond-mat.str-el· hep-lat· physics.atom-ph· quant-ph

Recognition: unknown

Dynamical preparation of U(1) quantum spin liquids in an analogue quantum simulator

Simon Karch , Melissa Will , Irene Prieto Rodriguez , Nikolas Liebster , SeungJung Huh , Michael Knap , Frank Pollmann , Clemens Kuhlenkamp

show 2 more authors

Immanuel Bloch Monika Aidelsburger

Authors on Pith no claims yet

Pith reviewed 2026-05-07 17:19 UTC · model grok-4.3

classification ❄️ cond-mat.quant-gas cond-mat.str-elhep-latphysics.atom-phquant-ph

keywords U(1) quantum spin liquidlattice gauge theoryultracold atomsoptical latticequantum simulationnon-equilibrium preparationgauge invarianceinterferometry

0 comments

The pith

Ultracold atoms in an optical superlattice dynamically prepare large regions of U(1) quantum spin liquids with observed many-body coherence.

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

This work shows how a two-dimensional U(1) lattice gauge theory can be realized on a large scale with over three thousand sites using ultracold atoms trapped in a square optical superlattice. The authors use dynamical quenches to prepare non-equilibrium states that exhibit features of quantum spin liquids, which are coherent superpositions of many different many-body configurations without conventional magnetic order. They validate the local gauge constraint through a quench and microscopy, and detect hallmark correlations in real and momentum space. Interferometric round-trip protocols then confirm extensive coherence across roughly one hundred lattice sites, indicating the presence of these exotic entangled states.

Core claim

The paper claims that non-equilibrium preparation protocols in an analog quantum simulator can create and make observable extended U(1) quantum spin liquid regions, as evidenced by direct observation of large-scale coherence between many-body configurations in a system of over 3000 sites, along with supporting signatures like Gauss's law compliance and pinch points.

What carries the argument

Round-trip interferometric protocols that probe coherence between different many-body configurations while respecting the gauge constraints.

Load-bearing premise

The interpretation that the measured coherence and correlations arise from the quantum spin liquid's many-body superpositions rather than from experimental noise, finite size, or imperfect enforcement of the gauge constraints.

What would settle it

If repeating the round-trip interferometry on larger systems shows the coherence length saturating well below 100 sites or the signal vanishing, that would indicate the regions are not truly extended quantum spin liquids.

Figures

Figures reproduced from arXiv: 2604.24744 by Clemens Kuhlenkamp, Frank Pollmann, Immanuel Bloch, Irene Prieto Rodriguez, Melissa Will, Michael Knap, Monika Aidelsburger, Nikolas Liebster, SeungJung Huh, Simon Karch.

**Figure 1.** Figure 1: Effective 2D monomer-dimer model and preparation of U(1) quantum spin liquids. a, Schematic of the 2D monomer-dimer model, where occupied vertices are monomers (green circles) and doublons on links are dimers (blue ellipses). This effective model arises from the 2D Bose-Hubbard model with tunnel coupling J, on-site interaction U ≫ J, and staggered superlattice potential ∆ ≫ J, restricting the dynamics to s… view at source ↗

**Figure 2.** Figure 2: Probing constrained gauge dynamics in the monomer-dimer model. a, Schematic of the doublon-detection sequence, which converts doubly occupied sites into singly occupied sites prior to imaging. In the presence of a gravitational tilt, reducing the vertical lattice depth converts doublons into singlons with peak fidelity 98(1)%. The lower panel shows the conversion probability p2→1 and the survival probabili… view at source ↗

**Figure 3.** Figure 3: Non-equilibrium preparation of U(1) quantum spin liquids. a, Schematic energy spectrum as a function of monomer mass m. For large negative monomer mass m, the ground state is unique, with all vertices occupied by monomers and no dimers (left inset). For large positive m, the lowest-energy states form a nearly degenerate manifold of dimer coverings {|di⟩} (right inset), with small splittings arising from… view at source ↗

**Figure 4.** Figure 4: Experimental preparation of U(1) QSLs. a, Representative experimental snapshot after the forward ramp, with a 35×35-site ROI indicated. Blue shading marks domains of near-perfect dimer covering consistent with the RK wavefunction; red shading marks regions containing monomers and Gauss’s law defects. The probability of a vertex occupied by a single monomer with no attached dimers is 14.9(1)%, and the proba… view at source ↗

**Figure 5.** Figure 5: Round-trip probe for many-body coherence. a, Schematic of the round-trip interferometric protocol (top). The coupling Jeff (red) is switched on in 1.8 ms and then, the mass is ramped forward into the QSL state. Phase imprinting is optionally applied and the forward ramp is then reversed. Selected fluorescence images (bottom) show the optimal round-trip, in which large initial monomer state domains emerge (… view at source ↗

**Figure 6.** Figure 6: Length scale of the QSL regions. a, Subsystem return probability L evaluated from round-trip snapshots [Tforward = Treverse = 6.35(3) ℏ/J] as a function of the subsystem area A, for rectangular subsystems such as the one illustrated in the inset (left). The normalised subsystem return probability − 1 A ln L (right) saturates to a constant (dashed line) for subsystems larger than the crossover area Ac, e… view at source ↗

read the original abstract

Locally constrained gauge theories underpin our understanding of fundamental interactions in particle physics and the emergent behaviour of quantum materials. In strongly correlated systems, they can give rise to quantum spin liquids that lack conventional order and are defined by coherent superpositions of an extensive number of many-body configurations. Realising and probing such exotic states experimentally is an outstanding challenge both in solid-state and synthetic quantum systems, not least due to the difficulty of detecting the fragile coherences between many-body states. Here, we report a large-scale (>3,000 sites) realisation of a two-dimensional U(1) lattice gauge theory with ultracold atoms in a square optical superlattice and demonstrate non-equilibrium preparation of extended regions of U(1) quantum spin liquids. We demonstrate Gauss's law validity in a quench experiment, enabled by a new microscopy technique for detecting doubly occupied sites. We observe characteristic real-space correlations and momentum-space pinch points, hallmarks of the emergent U(1) gauge structure. Using round-trip interferometric protocols, we directly observe large-scale coherence between many-body configurations, providing strong evidence for quantum spin liquid regions extending over ~100 lattice sites. Our results establish non-equilibrium quantum simulation protocols as a powerful route for accessing and probing exotic, highly-entangled states beyond those hosted by the engineered Hamiltonian in thermal equilibrium.

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

This paper shows a scaled-up dynamical preparation of U(1) quantum spin liquids in cold atoms, with direct interferometric coherence over ~100 sites as the main advance.

read the letter

This experiment shows a dynamical way to prepare extended U(1) quantum spin liquid regions in a large cold-atom simulator and backs it with direct coherence measurements over roughly 100 sites. They set up a two-dimensional U(1) lattice gauge theory using ultracold atoms in a square optical superlattice with more than 3000 sites. The preparation relies on quench dynamics rather than equilibrium. A new microscopy technique detects doubly occupied sites to confirm Gauss's law holds in quench experiments. They measure real-space correlations and momentum-space pinch points as indicators of the emergent gauge structure. The key addition is round-trip interferometry that reveals large-scale coherence between many-body configurations. This stands out for scaling the system and using non-equilibrium methods to reach states that might not be stable in the ground state. The coherence probe directly tackles the challenge of detecting fragile superpositions in these systems, which is a real strength. The softer part is whether the coherence unambiguously signals the QSL character. The stress-test concern is reasonable: the constraint check is separate from the interferometry, so residual gauge violations could contribute to the visibility without it being a true many-body superposition in the gauge-invariant sector. The abstract calls it strong evidence, but the full analysis would need to quantify how well the constraint is maintained during those specific runs to close off alternative explanations like finite-size effects or classical correlations. People in quantum simulation of condensed matter and gauge theories would get the most from this. It is worth bringing to a reading group for discussion on experimental techniques for entangled phases. The work merits peer review because it reports substantial experimental progress that the community should evaluate carefully.

Referee Report

1 major / 2 minor

Summary. The manuscript reports a large-scale (>3000 sites) experimental realization of a 2D U(1) lattice gauge theory using ultracold atoms in a square optical superlattice. It demonstrates non-equilibrium dynamical preparation of extended U(1) quantum spin liquid regions, validates Gauss's law via a new microscopy technique detecting double occupancies, observes real-space correlations and momentum-space pinch points as signatures of the emergent gauge structure, and employs round-trip interferometric protocols to directly measure large-scale coherence between many-body configurations, interpreted as evidence for QSL regions spanning ~100 lattice sites.

Significance. If the central claims on coherence and gauge structure hold, this work would be significant for quantum simulation of gauge theories and frustrated magnetism. It establishes scalable non-equilibrium protocols for preparing and probing highly entangled states inaccessible in equilibrium, with direct many-body coherence measurements and a new detection method for constraint violations. The system size enables observation of extended regions, providing a platform for studying emergent U(1) physics.

major comments (1)

[Abstract and interferometric protocol results] The central claim of QSL regions extending over ~100 lattice sites rests on the round-trip interferometric visibility (abstract and main results on interferometry). The protocol is stated to project onto the gauge-invariant subspace, but the manuscript validates Gauss's law only in a separate quench experiment using the new microscopy; no spatially resolved constraint-fidelity data are tied to the specific interferometry runs. This leaves open the possibility that observed coherence arises from mixtures with residual gauge violations (e.g., percent-level double occupancies or hopping-induced defects) rather than pure many-body superpositions within the U(1) sector, directly affecting the interpretation of the ~100-site scale.

minor comments (2)

[Figures on momentum-space correlations] Figure clarity: the momentum-space pinch-point plots would benefit from explicit overlays of theoretical pinch-point locations or quantitative line cuts to allow direct comparison with the observed features.
[Methods or results on interferometry] Notation: the definition of the round-trip interferometric phase or visibility metric should be stated explicitly with an equation, as it is central to the coherence claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their positive evaluation of the significance of our work and for the detailed and constructive comment. We address the concern about linking the interferometric coherence measurements to the Gauss-law validation below. We believe a partial revision, including clarifications and additional supporting analysis, will strengthen the manuscript.

read point-by-point responses

Referee: [Abstract and interferometric protocol results] The central claim of QSL regions extending over ~100 lattice sites rests on the round-trip interferometric visibility (abstract and main results on interferometry). The protocol is stated to project onto the gauge-invariant subspace, but the manuscript validates Gauss's law only in a separate quench experiment using the new microscopy; no spatially resolved constraint-fidelity data are tied to the specific interferometry runs. This leaves open the possibility that observed coherence arises from mixtures with residual gauge violations (e.g., percent-level double occupancies or hopping-induced defects) rather than pure many-body superpositions within the U(1) sector, directly affecting the interpretation of the ~100-site scale.

Authors: We appreciate the referee raising this point on the interpretation of the interferometric visibility. The round-trip protocol is constructed to measure many-body coherence by evolving the prepared state forward under the gauge-theory Hamiltonian and then reversing the evolution to project back onto the initial configuration; only components within the gauge-invariant subspace contribute constructively to the observed interference. The preparation sequence for the extended U(1) regions is identical in both the quench and interferometry experiments, and the new microscopy technique was used to characterize the dominant gauge violations (double occupancies) under these conditions. In the revised manuscript we will add a dedicated paragraph and supplementary figure that directly compares the double-occupancy fractions measured in the interferometry datasets with those from the quench runs, showing they remain at the sub-percent level. We will also note that any significant residual gauge violations would introduce defects that do not participate coherently in the round-trip interference, thereby reducing visibility; the high observed visibility is therefore inconsistent with substantial mixing outside the U(1) sector. While we do not possess run-by-run spatially resolved constraint maps for every interferometry realization, the aggregate statistics and identical preparation conditions provide a robust link between the two datasets. revision: partial

Circularity Check

0 steps flagged

No significant circularity: purely experimental report with no derivation chain

full rationale

This is an experimental paper reporting the realization of a 2D U(1) lattice gauge theory and non-equilibrium preparation of U(1) quantum spin liquid regions in an ultracold-atom simulator. The central results rest on direct observations: a new microscopy technique to validate Gauss's law via quench dynamics, real-space correlations, momentum-space pinch points, and round-trip interferometry to detect large-scale coherence over ~100 sites. No theoretical derivation, prediction, or ansatz is presented that reduces by the paper's own equations to a fitted parameter, self-referential quantity, or self-citation chain. All claims are grounded in measured data and established experimental protocols rather than internal mathematical closure. The report is therefore self-contained against external benchmarks with no load-bearing circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that the ultracold-atom optical superlattice accurately implements the target U(1) lattice gauge theory and that the interferometric signal faithfully reports many-body coherence of the spin liquid. No new free parameters or invented entities are introduced.

axioms (2)

domain assumption The engineered optical superlattice and interactions realize the desired two-dimensional U(1) lattice gauge theory
Invoked in the description of the experimental platform and quench protocol.
domain assumption The observed pinch points and interferometric coherence are signatures of the emergent U(1) gauge structure rather than artifacts
Central to interpreting the data as evidence for quantum spin liquid regions.

pith-pipeline@v0.9.0 · 5577 in / 1507 out tokens · 125939 ms · 2026-05-07T17:19:04.281644+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

69 extracted references · 12 canonical work pages · 2 internal anchors

[1]

Savary and L

L. Savary and L. Balents, Rep. Prog. Phys.80, 016502 (2017)

2017
[2]

Wen,Quantum Field Theory of Many-Body Sys- tems(Oxford University Press, 2007)

X.-G. Wen,Quantum Field Theory of Many-Body Sys- tems(Oxford University Press, 2007)

2007
[3]

Anderson, Mater

P. Anderson, Mater. Res. Bull.8, 153 (1973)

1973
[4]

D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett.61, 2376 (1988)

1988
[5]

Moessner, S

R. Moessner, S. L. Sondhi, and E. Fradkin, Phys. Rev. B 65, 024504 (2001)

2001
[8]

Broholm, R

C. Broholm, R. J. Cava, S. A. Kivelson, D. G. Nocera, M. R. Norman, and T. Senthil, Science367, eaay0668 (2020). 1

2020
[9]

A. T. Breidenbach, A. C. Campello, J. Wen, H.-C. Jiang, D. M. Pajerowski, R. W. Smaha, and Y. S. Lee, Nat. Phys.21, 1957 (2025)

1957
[10]

A. O. Scheie, M. Lee, K. Wang, P. Laurell, E. S. Choi, D. Pajerowski, Q. Zhang, J. Ma, H. D. Zhou, S. Lee, C. Huan, S. M. Thomas, M. O. Ajeesh, P. F. S. Rosa, A. Chen, V. S. Zapf, M. Heyl, C. D. Batista, E. Dagotto, J. E. Moore, and D. A. Tennant, arXiv:2406.17773 (2024)

work page arXiv 2024
[11]

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, Nature551, 579 (2017)

2017
[12]

F. M. Surace, P. P. Mazza, G. Giudici, A. Lerose, A. Gambassi, and M. Dalmonte, Phys. Rev. X10, 021041 (2020)

2020
[13]

B. Yang, H. Sun, R. Ott, H.-Y. Wang, T. V. Zache, J. C. Halimeh, Z.-S. Yuan, P. Hauke, and J.-W. Pan, Nature 587, 392 (2020)

2020
[14]

J. C. Halimeh, M. Aidelsburger, F. Grusdt, P. Hauke, and B. Yang, Nat. Phys.21, 25 (2025)

2025
[15]

Kebriˇ c, L

M. Kebriˇ c, L. Su, A. Douglas, M. Szurek, O. Markovi´ c, U. Schollw¨ ock, A. Bohrdt, M. Greiner, and F. Grusdt, arXiv:2509.16200 (2025)

work page arXiv 2025
[16]

P. R. Datla, L. Zhao, W. W. Ho, N. Klco, and H. Loh, Nat. Phys.22, 355 (2026)

2026
[17]

T. A. Cochranet al., Nature642, 315 (2025)

2025
[18]

Gonz´ alez-Cuadra, M

D. Gonz´ alez-Cuadra, M. Hamdan, T. V. Zache, B. Braverman, M. Kornjaˇ ca, A. Lukin, S. H. Cant´ u, F. Liu, S.-T. Wang, A. Keesling, M. D. Lukin, P. Zoller, and A. Bylinskii, Nature642, 321 (2025)

2025
[19]

Gyawali, S

G. Gyawaliet al., arXiv:2410.06557 (2024)

work page arXiv 2024
[20]

M. Meth, J. Zhang, J. F. Haase, C. Edmunds, L. Postler, A. J. Jena, A. Steiner, L. Dellantonio, R. Blatt, P. Zoller, T. Monz, P. Schindler, C. Muschik, and M. Ringbauer, Nat. Phys.21, 570 (2025)

2025
[21]

Digital quantum magnetism on a trapped-ion quantum computer

R. Haghshenaset al., arXiv:2503.20870 (2025)

work page internal anchor Pith review Pith/arXiv arXiv 2025
[22]

J. C. Halimeh, N. Mueller, J. Knolle, Z. Papi´ c, and Z. Davoudi, arXiv:2509.03586 (2025)

work page arXiv 2025
[23]

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, Science 374, 1242 (2021)

2021
[24]

K. J. Satzingeret al., Science374, 1237 (2021)

2021
[25]

Zhou, G.-X

Z.-Y. Zhou, G.-X. Su, J. C. Halimeh, R. Ott, H. Sun, P. Hauke, B. Yang, Z.-S. Yuan, J. Berges, and J.-W. Pan, Science377, 311 (2022)

2022
[26]

Wang, W.-Y

H.-Y. Wang, W.-Y. Zhang, Z. Yao, Y. Liu, Z.-H. Zhu, Y.- G. Zheng, X.-K. Wang, H. Zhai, Z.-S. Yuan, and J.-W. Pan, Phys. Rev. Lett.131, 050401 (2023)

2023
[27]

J. J. Osborne, I. P. McCulloch, B. Yang, P. Hauke, and J. C. Halimeh, Commun. Phys.8, 273 (2025)

2025
[28]

Horn, Phys

D. Horn, Phys. Lett. B100, 149 (1981)

1981
[29]

Orland and D

P. Orland and D. Rohrlich, Nucl. Phys. B338, 647 (1990)

1990
[30]

Chandrasekharan and U.-J

S. Chandrasekharan and U.-J. Wiese, Nucl. Phys. B492, 455 (1997)

1997
[31]

Wiese, Ann

U.-J. Wiese, Ann. Phys.525, 777 (2013)

2013
[32]

Dalmonte and S

M. Dalmonte and S. Montangero, Contemp. Phys.57, 388 (2016)

2016
[33]

Giudici, M

G. Giudici, M. D. Lukin, and H. Pichler, Phys. Rev. Lett. 129, 090401 (2022)

2022
[34]

Sahay, A

R. Sahay, A. Vishwanath, and R. Verresen, arXiv:2211.01381 (2023)

work page arXiv 2023
[35]

N. O. Gjonbalaj, R. Sahay, and S. F. Yelin, arXiv:2502.03518 (2025)

work page arXiv 2025
[37]

S. V. Isakov, K. Gregor, R. Moessner, and S. L. Sondhi, Phys. Rev. Lett.93, 167204 (2004)

2004
[38]

Fennell, P

T. Fennell, P. P. Deen, A. R. Wildes, K. Schmalzl, D. Prabhakaran, A. T. Boothroyd, R. J. Aldus, D. F. McMorrow, and S. T. Bramwell, Science326, 415 (2009)

2009
[39]

D. J. P. Morris, D. A. Tennant, S. A. Grigera, B. Klemke, C. Castelnovo, R. Moessner, C. Czternasty, M. Meiss- ner, K. C. Rule, J.-U. Hoffmann, K. Kiefer, S. Gerischer, D. Slobinsky, and R. S. Perry, Science326, 411 (2009)

2009
[42]

Fradkin and S

E. Fradkin and S. Kivelson, Mod. Phys. Lett. B04, 225 (1990)

1990
[43]

W. S. Bakr, J. I. Gillen, A. Peng, S. F¨ olling, and M. Greiner, Nature462, 74 (2009)

2009
[44]

J. F. Sherson, C. Weitenberg, M. Endres, M. Cheneau, I. Bloch, and S. Kuhr, Nature467, 68 (2010)

2010
[45]

Gross and W

C. Gross and W. S. Bakr, Nat. Phys.17, 1316 (2021)

2021
[46]

L. Su, A. Douglas, M. Szurek, A. H. H´ ebert, A. Krahn, R. Groth, G. A. Phelps, O. Markovi´ c, and M. Greiner, Nat. Commun.16, 1017 (2025)

2025
[47]

S. T. Bramwell and M. J. P. Gingras, Science294, 1495 (2001)

2001
[48]

M. J. Harris, S. T. Bramwell, D. F. McMorrow, T. Zeiske, and K. W. Godfrey, Phys. Rev. Lett.79, 2554 (1997)

1997
[49]

A. P. Ramirez, A. Hayashi, R. J. Cava, R. Siddharthan, and B. S. Shastry, Nature399, 333 (1999)

1999
[50]

Pomaranski, L

D. Pomaranski, L. R. Yaraskavitch, S. Meng, K. A. Ross, H. M. L. Noad, H. A. Dabkowska, B. D. Gaulin, and J. B. Kycia, Nat. Phys.9, 353 (2013)

2013
[51]

M. J. P. Gingras, P. A. McClarty, and J. G. Rau, in Spin Ice, Vol. 197, edited by M. Udagawa and L. Jaubert (Springer International Publishing, Cham, 2021) pp. 1– 18

2021
[52]

B. Gao, F. Desrochers, D. W. Tam, D. M. Kirschbaum, P. Steffens, A. Hiess, D. H. Nguyen, Y. Su, S.-W. Cheong, S. Paschen, Y. B. Kim, and P. Dai, Nat. Phys.21, 1203 (2025)

2025
[54]

A. A. Geim, N. U. Koyluoglu, S. J. Evered, R. Sa- hay, S. H. Li, M. Xu, D. Bluvstein, N. O. Gjonbalaj, N. Maskara, M. Kalinowski, T. Manovitz, R. Verresen, S. F. Yelin, J. Feldmeier, M. Greiner, V. Vuletic, and M. D. Lukin, arXiv:2602.18555 (2026)

work page arXiv 2026
[55]

Dirac Spin Liquid Candidate in a Rydberg Quantum Simulator

G. Bornet, M. Bintz, C. Chen, G. Emperauger, D. Barredo, S. Chatterjee, V. S. Liu, T. Lahaye, M. P. Zaletel, N. Y. Yao, and A. Browaeys, arXiv:2602.14323 (2026). Supplementary Information for: Dynamical preparation ofU(1)quantum spin liquids in an analogue quantum simulator CONTENTS I. Experimental details 2 A. Experimental setup 2 B. Experimental sequenc...

work page internal anchor Pith review Pith/arXiv arXiv 2026
[56]

Initial state preparation. The initial state is prepared by first ramping the long lattices to 35E l r over 220 ms (atϕ∼ −0.05π), and then increasing the short lattice depth to 45E s r over 20 ms, lo- calizing the atoms at the lowest-energy site of the 2×2 unit cell. Here,E s,l r =h 2/(8ma2 s,l) is the recoil energy of the short and long horizontal lattic...
[57]

unphysical

Non-equilibrium dynamics. The diagonal tilt is implemented by applying a quadrupole field using a pair of coils along thez-direction and rotating the offset field into the diagonal direction in the horizontal plane. During this rotation, the offset field magnitude is also ramped up to 42.0 G, increasing the scattering length toa∼800a 0. The following expe...

2020
[58]

Impertro, J

A. Impertro, J. F. Wienand, S. H¨ afele, H. von Raven, S. Hubele, T. Klostermann, C. R. Cabrera, I. Bloch, and M. Aidelsburger, Commun. Phys.6, 1 (2023)

2023
[59]

J. F. Wienand, S. Karch, A. Impertro, C. Schweizer, E. McCulloch, R. Vasseur, S. Gopalakrishnan, M. Aidels- burger, and I. Bloch, Nat. Phys.20, 1732 (2024)

2024
[60]

Impertro, S

A. Impertro, S. Karch, J. F. Wienand, S. Huh, C. Schweizer, I. Bloch, and M. Aidelsburger, Phys. Rev. Lett.133, 063401 (2024)

2024
[61]

Impertro, S

A. Impertro, S. Huh, S. Karch, J. F. Wienand, I. Bloch, and M. Aidelsburger, Nat. Phys.21, 895 (2025)

2025
[62]

Karch, S

S. Karch, S. Bandyopadhyay, Z.-H. Sun, A. Impertro, S. Huh, I. P. Rodr´ ıguez, J. F. Wienand, W. Ketterle, M. Heyl, A. Polkovnikov, I. Bloch, and M. Aidelsburger, arXiv:2501.16995 (2025)

work page arXiv 2025
[63]

Serwane, G

F. Serwane, G. Z¨ urn, T. Lompe, T. B. Ottenstein, A. N. Wenz, and S. Jochim, Science332, 336 (2011)

2011
[64]

N. Jain, J. Zhang, M. Culemann, and P. M. Preiss, arXiv:2512.09849 (2025)

work page arXiv 2025
[65]

Gl¨ uck, A

M. Gl¨ uck, A. R. Kolovsky, and H. J. Korsch, Phys. Rev. Lett.83, 891 (1999)

1999
[66]

Zenesini, H

A. Zenesini, H. Lignier, G. Tayebirad, J. Radogostowicz, D. Ciampini, R. Mannella, S. Wimberger, O. Morsch, and E. Arimondo, Phys. Rev. Lett.103, 090403 (2009)

2009
[67]

Scherg, T

S. Scherg, T. Kohlert, P. Sala, F. Pollmann, B. Hebbe Madhusudhana, I. Bloch, and M. Aidelsburger, Nat. Commun.12, 4490 (2021)

2021
[68]

P. Sala, T. Rakovszky, R. Verresen, M. Knap, and F. Poll- mann, Phys. Rev. X10, 011047 (2020)

2020
[69]

Khemani, M

V. Khemani, M. Hermele, and R. Nandkishore, Phys. Rev. B101, 174204 (2020)

2020
[70]

Moudgalya, B

S. Moudgalya, B. A. Bernevig, and N. Regnault, Rep. Prog. Phys.85, 086501 (2022)

2022
[71]

Hauschild, J

J. Hauschild, J. Unfried, S. Anand, B. Andrews, M. Bintz, U. Borla, S. Divic, M. Drescher, J. Geiger, M. Hefel, K. H´ emery, W. Kadow, J. Kemp, N. Kirchner, V. S. Liu, G. M¨ oller, D. Parker, M. Rader, A. Romen, S. Scalet, L. Schoonderwoerd, M. Schulz, T. Soejima, P. Thoma, Y. Wu, P. Zechmann, L. Zweng, R. S. K. Mong, M. P. Zaletel, and F. Pollmann, SciPo...

work page doi:10.21468/scipostphyscodeb.41 2024
[72]

Moessner and K

R. Moessner and K. S. Raman, inIntroduction to Frustrated Magnetism: Materials, Experiments, Theory, edited by C. Lacroix, P. Mendels, and F. Mila (Springer Berlin Heidelberg, Berlin, Heidelberg, 2011) pp. 437–479

2011
[73]

Fradkin,Field Theories of Condensed Matter Physics, 2nd ed

E. Fradkin,Field Theories of Condensed Matter Physics, 2nd ed. (Cambridge University Press, 2013)

2013
[74]

Polyakov, Nucl

A. Polyakov, Nucl. Phys. B120, 429 (1977)

1977
[75]

D. S. Rokhsar and S. A. Kivelson, Phys. Rev. Lett.61, 2376 (1988). 15 a b 0 10 20 10 3 10 2 10 1 0 10 20 0 10 20 0 0.012 i cj Radial average of the correlations i cj Monomer-monomer correlations Distance (lattice sites)Dimer-dimer correlations-0.05 0.050 SH V H S V Figure S13.Dimer-dimer and monomer-monomer correlations for the columnar states. a,Dimer-di...

1988