Pith. sign in

REVIEW 4 major objections 5 minor 94 references

The paper claims that the ground state of the 2+1D SU(2) lattice gauge theory with staggered fermions undergoes a magnetic-flux transition at λ* ≈ −0.04 and a gauge–matter delocalization crossover along the physical line, as established by

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-01 00:40 UTC pith:EESWTPDS

load-bearing objection First untruncated continuous-group variational run for 2+1D SU(2)+dynamical fermions: the method is real, but the flux transition is currently variational hysteresis, not established physics. the 4 major comments →

arxiv 2607.26132 v1 pith:EESWTPDS submitted 2026-07-28 hep-lat cond-mat.quant-gascond-mat.str-elhep-phquant-ph

Quantum Phase Diagram of the 2+1D Untruncated SU(2) Lattice Gauge Theory with Dynamical Fermions

Gabriel Rouxinol , Julian Bender , Patrick Emonts , Michele Grossi , Jad C. Halimeh This is my paper
classification hep-lat cond-mat.quant-gascond-mat.str-elhep-phquant-ph
keywords lattice gauge theorySU(2) gauge groupdynamical fermionsvariational Monte Carlomagnetic flux transitiongauge-matter delocalizationchiral condensateGauss law
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper aims to determine the ground-state behavior of the 2+1D SU(2) lattice gauge theory with dynamical fermions, retaining the full continuous gauge group without truncation. Treating the magnetic and electric couplings as independent, it finds two locally stable magnetic-flux branches that cross near λ* = −0.040 ± 0.005, with no resolvable dependence on the electric coupling. Along the physical line λ = 4/g², it uncovers a crossover from a flux-disordered, Néel-like regime at strong electric coupling to an ordered unity-flux regime with delocalized matter at weak coupling. If correct, the work demonstrates that variational methods can access non-Abelian gauge–matter ground states beyond the reach of Euclidean Monte Carlo, opening a route to sign-problem-free studies of confinement and related phenomena.

Core claim

The central discovery is that, in the untruncated SU(2) lattice gauge theory with staggered fermions on L×L lattices (L = 4,6,8), the ground state organizes into two distinct flux sectors. For negative magnetic coupling λ, the system exhibits a transition at λ* ≈ −0.04 between a π-flux sector with ⟨cos B_p⟩ = −1 and a unity-flux sector with ⟨cos B_p⟩ = +1, with the transition point essentially independent of the electric coupling g². Along the physical line λ = 4/g², decreasing g² drives a crossover: the gauge field concentrates on unity-flux configurations, and the fermions delocalize from the Néel reference state, as signaled by the chiral condensate, a Wilson-line meson correlator, and th

What carries the argument

The key machinery is the variational wavefunction |Ψ⟩ = ∫ DU Ψ_G(U) |Ψ_F(U)⟩ |U⟩, where Ψ_G is a gauge wavefunction built from a Jastrow factor and a convolutional neural network, and |Ψ_F(U)⟩ is a gauge-covariant Gaussian fermionic state obtained by applying a unitary generated by short Wilson-line paths to the Néel reference. This construction guarantees gauge invariance and Gauss's law by construction, and all fermionic observables reduce to traces of the occupation matrix, enabling joint optimization of the gauge and matter sectors.

Load-bearing premise

The load-bearing premise is that the variational family—a neural-network gauge wavefunction combined with gauge-covariant Gaussian fermionic states—is expressive enough to capture the true ground state on L = 4, 6, 8; if the ansatz misses relevant correlations or the optimization gets stuck in a local minimum, the reported flux branches and crossover could be variational artifacts rather than properties of the exact model.

What would settle it

Perform a Binder-cumulant analysis of the intensive plaquette average across λ for L = 4, 6, 8 (and larger if possible); a crossing of the cumulants at λ* ≈ −0.04 would support a genuine phase transition, whereas strongly size-dependent curves without a common crossing would indicate the hysteresis is a variational or finite-size artifact.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • If the variational calculation is faithful, the magnetic-flux transition at λ* ≈ −0.04 is a genuine property of the untruncated model, stable against changes in the electric coupling across the explored range.
  • Along the physical line λ = 4/g², the ground state evolves continuously from a flux-disordered, Néel-localized regime to a unity-flux, delocalized regime as g² decreases, with chiral condensate, meson correlator, and local color density all tracking the same crossover.
  • The variational framework can be extended to other non-Abelian gauge theories with dynamical matter without truncating the gauge group, offering a route to regimes where Euclidean Monte Carlo suffers from the sign problem.
  • The authors argue this establishes a route toward first-principles studies of nonperturbative non-Abelian gauge–matter physics in regimes inaccessible to conventional Euclidean methods.

Where Pith is reading between the lines

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

  • If the transition is genuinely first-order and λ* is exactly g²-independent, the mechanism may reduce to a competition between Lieb-flux-favored and magnetic-favored sectors that is set entirely by the mass–hopping term; this could be tested by varying the fermion mass and checking whether λ* shifts accordingly.
  • The observed crossover along the physical line may sharpen into a true phase transition at larger system sizes; a susceptibility or Binder-cumulant analysis would distinguish a crossover from a transition.
  • Because the fermionic correction is Gaussian for each gauge configuration, non-Gaussian correlations (e.g., those needed for chiral symmetry breaking at zero mass) are beyond the current ansatz; extending the fermionic part to a neural-network parameterization might change the location or character of the crossover.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. This Letter presents a variational Monte Carlo study of the 2+1D SU(2) lattice gauge theory with staggered dynamical fermions, working directly in the magnetic basis with the full continuous gauge group and without truncating the electric-field Hilbert space. The variational ansatz (Eq. 2) combines a neural-network gauge wavefunction with gauge-covariant Gaussian fermionic states, and the two are optimized jointly. Treating the magnetic and electric couplings λ and g² as independent parameters, the authors report a magnetic-flux transition at λ* = −0.040 ± 0.005 between π-flux-like and unity-flux-like sectors, with no resolved dependence of λ* on g² for L = 4 and 6 (Figs. 2, S1, S2). Along the physical line λ = 4/g², they identify a gauge–matter delocalization crossover from a flux-disordered, Néel-like regime at strong electric coupling to a unity-flux, delocalized regime at weak coupling, as signaled by the plaquette average, chiral condensate, matter color density, and Wilson-line meson correlator (Fig. 3). The supplemental material documents the hysteresis extraction, the numerical test of the Lieb flux expectation, and the analytical formulas for the fermionic observables.

Significance. If the central results hold, this is a notable advance: it is the first variational treatment of an untruncated non-Abelian gauge theory with dynamical fermions in 2+1D, and it offers access to regimes where Euclidean Monte Carlo suffers from a sign problem. The paper is careful in several respects: the authors explicitly acknowledge that no definitive finite-size scaling is possible, they provide data and code availability, and they support the static-unity-link comparison with concrete free-fermion reference values C* and |G(r)|* rather than fitting them. The use of a Gaussian fermionic state superposed over gauge configurations is a principled way to preserve Gauss's law while keeping computational cost polynomial. Should the transition and crossover survive more stringent tests, the framework would open a credible route to ground-state studies of non-Abelian gauge–matter physics beyond current Euclidean methods.

major comments (4)
  1. [Results, Fig. 2, and Supplemental Sec. S2] The central flux-transition claim rests on hysteresis between two variational branches initialized in the ⟨cos Bp⟩ = ±1 sectors. Hysteresis of this kind is expected even if the true ground state has no first-order transition, because each optimizer can remain in the basin of its initialization. The only non-hysteretic evidence shown is the energy crossing at g² = 0 for L = 6 (Fig. 2b); no energy crossing is shown for L = 4 or for g² > 0. The estimator λ* is defined as the location of maximal branch separation, which has no demonstrated relation to the thermodynamic transition point, and its uncertainty includes only the local polynomial fit, not the systematic error from the estimator or from variational bias. At g² = 2 the hysteresis curves are nearly flat, making the maximum-separation estimator ill-conditioned. I request: (i) energy-crossing curves for L = 4 and for the nonzero g² val
  2. [Eq. (2), Sec. S1, and variational-bias discussion] The load-bearing premise is that the ansatz of Eq. (2), with O(L^4) variational parameters, is expressive enough and the joint optimization finds near-ground states on the system sizes used. The paper does not quantify this variational bias. The adversarial search in Sec. S1 tests only the free-fermion Hamiltonian h_MH on static gauge configurations sampled from 8000 Haar-random configurations; it does not test the full variational state or the full Hamiltonian, and it cannot exclude energetically relevant gauge configurations near the transition. The Lieb flux-phase theorem is proved for Abelian flux on bipartite lattices, so its extension to SU(2) at m/t = 0.5 is an assumption that is only partially tested. These points do not invalidate the results, but they mean the transition is currently a plausible variational finding rather than a property established for the exact model. Please
  3. [Results, Fig. 2(c), and Summary] The transition point is extracted only from L = 4 and L = 6, with no L = 8 data for the flux transition, and the authors explicitly state that finite-size scaling is not accessible. For a first-order transition, hysteresis width and the location of the maximum-separation estimator generally depend on system size and protocol; without FSS, the quoted λ* = −0.040 ± 0.005 should be regarded as a finite-size variational estimate. The statement in the Summary that the results provide 'evidence consistent with a phase transition' is appropriately hedged, but the abstract's unqualified 'we find a magnetic-flux transition' overstates the evidence. Please either soften the abstract or add a finite-size analysis (even a partial L = 8 flux scan) that would justify the phase-transition terminology.
  4. [Fig. 3 and physical-line crossover] The gauge–matter delocalization crossover is inferred from monotonic trends of C, |S|², and |G(r)| with g², without a defined crossover scale or finite-size collapse. The authors call this a crossover rather than a transition, which is consistent with the data, but the claim 'crossover' should be supported by at least a heuristic crossover criterion (e.g., the g² value where C departs from its Néel value by a specified fraction, or where ⟨cos Bp⟩ reaches 1/2). The free-fermion references C* and |G(r)|* are computed in the thermodynamic limit at U = I, whereas the variational data are at L = 4, 6, 8; the agreement is shown only by visual inspection. A quantitative finite-size extrapolation toward the g² → 0 limit would make the crossover claim more robust.
minor comments (5)
  1. [Model and Eq. (2)] The symbol U is used both for the full set of links and for an integration variable in D U. This is standard but can be confusing; consider using a different symbol for the link configuration in Eq. (2).
  2. [Fig. 1 and text near Eq. (1)] The term 'unity-flux sector' is used for ⟨cos Bp⟩ ≈ 1. Since the plaquette term is 1 − (1/2)Tr P, ⟨cos Bp⟩ = 1 corresponds to trivial holonomy, not to one unit of conventional magnetic flux. Please define this terminology at first use to avoid confusion with the π-flux sector.
  3. [Supplemental Sec. S1] The adversarial search is described as comparing 8000 Haar-random configurations spanning L ∈ {4,6,8}, but the number per lattice size is not stated. Please specify how many configurations were used for each L and whether the same set was used for all mass-to-hopping ratios.
  4. [Companion reference [89]] The variational ansatz, the neural-network architecture, the optimization details, and the benchmarks are deferred to the companion paper [89]. Since the present Letter's conclusions depend on those details, the Supplemental Material should include at least a summary of the network architecture, the number of parameters, and the optimization hyperparameters so that the work is self-contained.
  5. [Minor text issues] There are a few typographical issues in the figure axes (e.g., '10□1' appears to be a rendering artifact for '10^{-1}'), and the phrase 'no resolvable drift' is used where 'no resolved dependence' would be more precise. These do not affect the physics.

Circularity Check

0 steps flagged

No significant circularity: the phase-diagram claims are outputs of an optimized variational ansatz with independent exact-limit checks; self-citations are methodological, and the C=⟨H_m⟩/(mN) identity is bookkeeping, not a derived prediction.

full rationale

The central results (λ*≈−0.040, no resolvable g² drift, and the crossover observables) are computed outputs of the joint optimization of Ψ_G(U) and |Ψ_F(U)⟩ in Eq. (2), not parameters fitted to a target. The transition estimate λ* is defined as the location of maximum separation between two variational branches and is cross-checked at g²=0 by an independent energy crossing λ_E=−0.039 (Fig. 2b), so it is not a fitted input dressed as a prediction. The C* and |G(r)|* reference values are obtained by diagonalizing the static unity-link free-fermion problem h_MH(U=I), external to the variational data. The identity C=⟨H_m⟩/(mN) noted in Sec. S3 is explicitly acknowledged and is a bookkeeping identity, not a derivation of one physical quantity from another. Self-citations to companion [89] provide algorithmic construction and benchmarks, while [81] and [83] are prior independent methodological foundations; none is invoked as a uniqueness theorem forcing the physical conclusions. The paper itself states that finite-size scaling beyond L=4,6,8 would be needed to determine the transition exactly, which is a limitation rather than a circular step. Overall, no load-bearing step reduces to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 4 axioms · 0 invented entities

No new particles, forces, dimensions, or symmetries are postulated. The model uses standard lattice Hamiltonian parameters (t=1.0, m=0.5, λ, g²) with no constants fitted to external data. The main unstated input is the variational expressiveness assumption and the non-Abelian extension of Lieb's theorem, each noted in the text.

axioms (4)
  • domain assumption The Kogut–Susskind Hamiltonian with staggered fermions (Eq. 1) is the correct UV description of the 2+1D SU(2) gauge theory with dynamical matter.
    Standard model formulation; not derived in this paper.
  • domain assumption The variational ansatz of Eq. (2) — a superposition of gauge configurations with gauge-covariant Gaussian fermionic states — is expressive enough to represent the true ground state at L=4,6,8.
    Central premise; justified by benchmarks in companion [89] and internal consistency, but variational bias is not quantified here.
  • ad hoc to paper Lieb's flux-phase theorem, proved for Abelian flux on bipartite lattices, extends to SU(2) at m/t=0.5 in the thermodynamic limit, so U=I minimizes the mass–hopping energy.
    Explicitly tested in SM S1; violations at L=4 (5.4% of configurations up to 1% lower energy) show the assumption is not exact at small sizes; the paper assumes the violation vanishes with L.
  • domain assumption In the limit g²→0 the gauge distribution concentrates on static classical configurations and the fermionic problem reduces to free fermions governed by h_MH(U).
    Used to set the reference values C* and |G(r)|* for comparison with the variational data.

pith-pipeline@v1.3.0-alltime-deepseek · 16657 in / 11088 out tokens · 103659 ms · 2026-08-01T00:40:26.202851+00:00 · methodology

0 comments
read the original abstract

Non-Abelian gauge theories with dynamical matter govern the strong interaction and a broad class of strongly correlated quantum systems, yet their ground-state properties remain difficult to obtain from first principles. Using a continuous-group variational Monte Carlo approach that retains the full SU$(2)$ gauge field without truncation, we determine the ground-state behavior of the SU$(2)$ lattice gauge theory with staggered fermions on an $L\times L$ square lattice. Treating the magnetic and electric couplings $\lambda$ and $g^2$ independently, we find a magnetic-flux transition at $\lambda^\ast=-0.040\pm 0.005$, with no resolvable drift of the transition point as the electric coupling is varied. Along the physical coupling line $\lambda=4/g^2$, for $L=4,6,8$, we uncover a gauge-matter delocalization crossover from a flux-disordered regime at strong electric coupling to an ordered unity-flux regime at weak coupling. The chiral condensate, a gauge-invariant Wilson-line meson correlator, and the local color density consistently reveal the emergence of coherent gauge-assisted matter dynamics. Together, these results provide a unified physical picture of how magnetic-flux ordering and fermionic coherence develop in an untruncated non-Abelian lattice gauge theory.

Figures

Figures reproduced from arXiv: 2607.26132 by Gabriel Rouxinol, Jad C. Halimeh, Julian Bender, Michele Grossi, Patrick Emonts.

Figure 1
Figure 1. Figure 1: FIG. 1. Variational framework, model, and principal phys [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Magnetic-flux transition between sectors with [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Ground-state observables along the physical line [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

discussion (0)

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

Reference graph

Works this paper leans on

94 extracted references · 8 linked inside Pith

  1. [1]

    Weinberg,The Quantum Theory of Fields(Cambridge University Press, 1995)

    S. Weinberg,The Quantum Theory of Fields(Cambridge University Press, 1995)

    1995

  2. [2]

    Peskin and D

    M. Peskin and D. Schroeder,An Introduction To Quan- tum Field Theory(CRC Press, 2018)

    2018

  3. [3]

    Srednicki,Quantum Field Theory(Cambridge Uni- versity Press, 2007)

    M. Srednicki,Quantum Field Theory(Cambridge Uni- versity Press, 2007)

    2007

  4. [4]

    K. G. Wilson, Physical Review D10, 2445 (1974)

    1974

  5. [5]

    D. J. Gross, Physical Review D8, 3633 (1973)

    1973

  6. [6]

    X. Wen,Quantum Field Theory of Many-Body Sys- tems:From the Origin of Sound to an Origin of Light and Electrons: From the Origin of Sound to an Origin of Light and Electrons, Oxford Graduate Texts (OUP Oxford, 2004)

    2004

  7. [7]

    Balents, Nature464, 199 (2010)

    L. Balents, Nature464, 199 (2010)

    2010

  8. [8]

    Savary and L

    L. Savary and L. Balents, Reports on Progress in Physics 80, 016502 (2016-11)

    2016

  9. [9]

    Fradkin,Field Theories of Condensed Matter Physics (Cambridge University Press, 2013)

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

    2013

  10. [10]

    Affleck and J

    I. Affleck and J. B. Marston, Physical Review B37, 3774 (1988)

    1988

  11. [11]

    X. G. Wen, Physical Review B44, 2664 (1991)

    1991

  12. [12]

    P. A. Lee, N. Nagaosa, and X.-G. Wen, Reviews of Mod- ern Physics78, 17 (2006)

    2006

  13. [13]

    Smith, J

    A. Smith, J. Knolle, R. Moessner, and D. L. Kovrizhin, Phys. Rev. Lett.119, 176601 (2017)

    2017

  14. [14]

    Brenes, M

    M. Brenes, M. Dalmonte, M. Heyl, and A. Scardicchio, Phys. Rev. Lett.120, 030601 (2018)

    2018

  15. [15]

    Budde, M

    T. Budde, M. Krstic Marinkovic, and J. C. Pinto Barros, Phys. Rev. D110, 094506 (2024)

    2024

  16. [16]

    Osborne, I

    J. Osborne, I. P. McCulloch, and J. C. Halimeh, Quan- tum Many-Body Scarring in 2 + 1D Gauge Theories with Dynamical Matter (2024), arXiv:2403.08858 [cond- mat.quant-gas]

    Pith/arXiv arXiv 2024

  17. [17]

    Cataldi, G

    G. Cataldi, G. Calaj´ o, P. Silvi, S. Montangero, and J. C. Halimeh, Phys. Rev. Lett.136, 170401 (2026)

    2026

  18. [18]

    Banerjee, M

    D. Banerjee, M. B¨ ogli, M. Dalmonte, E. Rico, P. Stebler, U.-J. Wiese, and P. Zoller, Physical Review Letters110, 125303 (2013)

    2013

  19. [19]

    Tagliacozzo, A

    L. Tagliacozzo, A. Celi, P. Orland, M. W. Mitchell, and M. Lewenstein, Nature Communications4, 2615 (2013)

    2013

  20. [20]

    Cataldi, S

    G. Cataldi, S. Orlando, and J. C. Halimeh, Real- Time String Dynamics in a 2 + 1D Non-Abelian Lat- tice Gauge Theory: String Breaking, Glueball Forma- tion, Baryon Blockade, and Tension Reduction (2025), arXiv:2509.08868 [hep-lat]

    arXiv 2025

  21. [21]

    Y. Y. Atas, J. Zhang, R. Lewis, A. Jahanpour, J. F. Haase, and C. A. Muschik, Nature Communications12, 6499 (2021)

    2021

  22. [22]

    M. J. Teper, Physical Review D59, 014512 (1998)

    1998

  23. [23]

    Karabali and V

    D. Karabali and V. P. Nair, Nuclear Physics B464, 135 (1996)

    1996

  24. [24]

    R. P. Feynman, Nuclear Physics B188, 479 (1981)

    1981

  25. [25]

    Fodor and S

    Z. Fodor and S. D. Katz, Physics Letters B534, 87 (2002)

    2002

  26. [26]

    Troyer and U.-J

    M. Troyer and U.-J. Wiese, Physical Review Letters94, 170201 (2005)

    2005

  27. [27]

    Vicari and H

    E. Vicari and H. Panagopoulos, Physics Reports470, 93 6 (2009)

    2009

  28. [28]

    Philipsen, The European Physical Journal Special Topics152, 29 (2007)

    O. Philipsen, The European Physical Journal Special Topics152, 29 (2007)

    2007

  29. [29]

    Kogut and L

    J. Kogut and L. Susskind, Physical Review D11, 395 (1975)

    1975

  30. [30]

    M. C. Ba˜ nuls, R. Blatt, J. Catani, A. Celi, J. I. Cirac, M. Dalmonte, L. Fallani, K. Jansen, M. Lewenstein, S. Montangero, C. A. Muschik, B. Reznik, E. Rico, L. Tagliacozzo, K. Van Acoleyen, F. Verstraete, U.-J. Wiese, M. Wingate, J. Zakrzewski, and P. Zoller, The European Physical Journal D74, 165 (2020)

    2020

  31. [31]

    Byrnes and Y

    T. Byrnes and Y. Yamamoto, Physical Review A73, 022328 (2006)

    2006

  32. [32]

    Dalmonte and S

    M. Dalmonte and S. Montangero, Con- temporary Physics57, 388 (2016), eprint: https://doi.org/10.1080/00107514.2016.1151199

    arXiv 2016

  33. [33]

    Zohar, J

    E. Zohar, J. I. Cirac, and B. Reznik, Reports on Progress in Physics79, 014401 (2015)

    2015

  34. [34]

    Aidelsburger, L

    M. Aidelsburger, L. Barbiero, A. Bermudez, T. Chanda, A. Dauphin, D. Gonz´ alez-Cuadra, P. R. Grzybowski, S. Hands, F. Jendrzejewski, J. J¨ unemann, G. Juzeli¯ unas, V. Kasper, A. Piga, S.-J. Ran, M. Rizzi, G. Sierra, L. Tagliacozzo, E. Tirrito, T. V. Zache, J. Zakrzewski, E. Zohar, and M. Lewenstein, Philosophical Transactions of the Royal Society A: Mat...

    2021

  35. [35]

    Zohar, Philosophical Transactions of the Royal Soci- ety A: Mathematical, Physical and Engineering Sciences 380, 20210069 (2021)

    E. Zohar, Philosophical Transactions of the Royal Soci- ety A: Mathematical, Physical and Engineering Sciences 380, 20210069 (2021)

    2021

  36. [36]

    Barata, X

    J. Barata, X. Du, M. Li, W. Qian, and C. A. Salgado, Physical Review D106, 074013 (2022)

    2022

  37. [37]

    N. Klco, A. Roggero, and M. J. Savage, Reports on Progress in Physics85, 064301 (2022)

    2022

  38. [38]

    Barata, X

    J. Barata, X. Du, M. Li, W. Qian, and C. A. Salgado, Physical Review D108, 056023 (2023)

    2023

  39. [39]

    Barata, W

    J. Barata, W. Gong, and R. Venugopalan, Physical Re- view D109, 116003 (2024)

    2024

  40. [40]

    C. W. Bauer, Z. Davoudi, A. B. Balantekin, T. Bhat- tacharya, M. Carena, W. A. de Jong, P. Draper, A. El-Khadra, N. Gemelke, M. Hanada, D. Kharzeev, H. Lamm, Y.-Y. Li, J. Liu, M. Lukin, Y. Meurice, C. Monroe, B. Nachman, G. Pagano, J. Preskill, E. Ri- naldi, A. Roggero, D. I. Santiago, M. J. Savage, I. Sid- diqi, G. Siopsis, D. Van Zanten, N. Wiebe, Y. Ya...

    2023

  41. [41]

    C. W. Bauer, Z. Davoudi, N. Klco, and M. J. Savage, Nature Reviews Physics5, 420 (2023)

    2023

  42. [42]

    Di Meglio, PRX Quantum5, 10.1103/PRXQuan- tum.5.037001 (2024)

    A. Di Meglio, PRX Quantum5, 10.1103/PRXQuan- tum.5.037001 (2024)

    doi:10.1103/prxquan- 2024

  43. [43]

    Cheng and H

    Y. Cheng and H. Zhai, Nature Reviews Physics6, 566 (2024)

    2024

  44. [44]

    T. D. Cohen, H. Lamm, S. Lawrence, and Y. Yamauchi (NuQS Collaboration), Phys. Rev. D104, 094514 (2021)

    2021

  45. [45]

    Barata and S

    J. Barata and S. Mukherjee, Phys. Rev. D111, L031901 (2025)

    2025

  46. [46]

    K. Lee, F. Turro, and X. Yao, Physical Review D111, 054514 (2025)

    2025

  47. [47]

    Turro, A

    F. Turro, A. Ciavarella, and X. Yao, Physical Review D 109, 114511 (2024)

    2024

  48. [48]

    J. C. Halimeh, M. Aidelsburger, F. Grusdt, P. Hauke, and B. Yang, Nature Physics21, 25 (2025)

    2025

  49. [49]

    C. W. Bauer, Journal of High Energy Physics2025, 108 (2025)

    2025

  50. [50]

    J. C. Halimeh, N. Mueller, J. Knolle, Z. Papi´ c, and Z. Davoudi, Quantum simulation of out-of-equilibrium dynamics in gauge theories (2025)

    2025

  51. [51]

    E. Rico, T. Pichler, M. Dalmonte, P. Zoller, and S. Mon- tangero, Physical Review Letters112, 201601 (2014)

    2014

  52. [52]

    M. C. Ba˜ nuls, K. Cichy, J. I. Cirac, K. Jansen, and S. K¨ uhn, Physical Review X7, 041046 (2017)

    2017

  53. [53]

    Magnifico, G

    G. Magnifico, G. Cataldi, M. Rigobello, P. Majcen, D. Jaschke, P. Silvi, and S. Montangero, Communica- tions Physics8, 322 (2025)

    2025

  54. [54]

    Emonts, A

    P. Emonts, A. Kelman, U. Borla, S. Moroz, S. Gazit, and E. Zohar, Physical Review D107, 014505 (2023)

    2023

  55. [55]

    Or´ us, Annals of Physics349, 117 (2014)

    R. Or´ us, Annals of Physics349, 117 (2014)

    2014

  56. [56]

    Cataldi, Hamiltonian Lattice Gauge Theories: emer- gent properties from Tensor Network methods (2025), arXiv:2501.11115 [hep-lat]

    G. Cataldi, Hamiltonian Lattice Gauge Theories: emer- gent properties from Tensor Network methods (2025), arXiv:2501.11115 [hep-lat]

    Pith/arXiv arXiv 2025

  57. [57]

    Felser, P

    T. Felser, P. Silvi, M. Collura, and S. Montangero, Phys- ical Review X10, 041040 (2020)

    2020

  58. [58]

    Cataldi, G

    G. Cataldi, G. Magnifico, P. Silvi, and S. Montangero, Physical Review Research6, 033057 (2024)

    2024

  59. [59]

    Gyawali, S

    G. Gyawali, S. Kumar, Y. D. Lensky, E. Rosenberg, A. Szasz, T. Cochran, R. Chen, A. H. Karamlou, K. Kechedzhi, J. Berndtsson, T. Westerhout, A. As- faw, D. Abanin, R. Acharya, L. A. Beni, T. I. Ander- sen, M. Ansmann, F. Arute, K. Arya, N. Astrakhant- sev, J. Atalaya, R. Babbush, B. Ballard, J. C. Bardin, A. Bengtsson, A. Bilmes, G. Bortoli, A. Bourassa, ...

    Pith/arXiv arXiv 2025

  60. [60]

    T. A. Cochran, B. Jobst, E. Rosenberg, Y. D. Lensky, G. Gyawali, N. Eassa, M. Will, A. Szasz, D. Abanin, R. Acharya, L. Aghababaie Beni, T. I. Andersen, M. Ansmann, F. Arute, K. Arya, A. Asfaw, J. Ata- laya, R. Babbush, B. Ballard, J. C. Bardin, A. Bengts- son, A. Bilmes, A. Bourassa, J. Bovaird, M. Broughton, D. A. Browne, B. Buchea, B. B. Buckley, T. Bu...

    2025

  61. [61]

    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

  62. [62]

    Crippa, K

    A. Crippa, K. Jansen, and E. Rinaldi, Analysis of the con- finement string in (2 + 1)-dimensional Quantum Electro- dynamics with a trapped-ion quantum computer (2024), arXiv:2411.05628 [hep-lat]

    Pith/arXiv arXiv 2024

  63. [63]

    Cobos, J

    J. Cobos, J. Fraxanet, C. Benito, F. di Marcanto- nio, P. Rivero, K. Kap´ as, M. A. Werner, ¨O. Leg- eza, A. Bermudez, and E. Rico, Real-Time Dynam- ics in a (2+1)-D Gauge Theory: The Stringy Na- ture on a Superconducting Quantum Simulator (2025), arXiv:2507.08088 [quant-ph]

    Pith/arXiv arXiv 2025

  64. [64]

    K. Xu, U. Borla, S. Moroz, and J. C. Halimeh, String Breaking Dynamics and Glueball Formation in a 2 + 1D Lattice Gauge Theory (2025), arXiv:2507.01950 [hep-lat]

    Pith/arXiv arXiv 2025

  65. [65]

    Joshi, Y

    R. Joshi, Y. Tian, K. Hemery, N. S. Srivatsa, J. J. Os- borne, H. Dreyer, E. Rinaldi, and J. C. Halimeh, Ob- servation of genuine 2 + 1D string dynamics in a U(1) lattice gauge theory with a tunable plaquette term on a trapped-ion quantum computer (2026), arXiv:2604.07436 [quant-ph]

    Pith/arXiv arXiv 2026

  66. [66]

    E. A. Martinez, C. A. Muschik, P. Schindler, D. Nigg, A. Erhard, M. Heyl, P. Hauke, M. Dalmonte, T. Monz, P. Zoller, and R. Blatt, Nature534, 516 (2016)

    2016

  67. [67]

    Carleo and M

    G. Carleo and M. Troyer, Science355, 602 (2017)

    2017

  68. [68]

    W. L. McMillan, Physical Review138, A442 (1965)

    1965

  69. [69]

    Arisue, M

    H. Arisue, M. Kato, and T. Fujiwara, Progress of Theo- retical Physics70, 229 (1983)

    1983

  70. [70]

    S. A. Chin, O. S. van Roosmalen, E. A. Umland, and S. E. Koonin, Physical Review D31, 3201 (1985)

    1985

  71. [71]

    Medvidovi´ c and J

    M. Medvidovi´ c and J. R. Moreno, The European Physical Journal Plus139, 631 (2024)

    2024

  72. [72]

    D. Pfau, S. Axelrod, H. Sutterud, I. von Glehn, and J. S. Spencer, Science385, eadn0137 (2024)

    2024

  73. [73]

    Y. Wu, X. Xu, D. Poletti, Y. Fan, C. Guo, and H. Shang, Mathematics11, 1417 (2023)

    2023

  74. [74]

    Y. Wu, C. Guo, Y. Fan, P. Zhou, and H. Shang, inPro- ceedings of the International Conference for High Per- formance Computing, Networking, Storage and Analy- sis, SC ’23 (Association for Computing Machinery, New York, NY, USA, 2023) pp. 1–13

    2023

  75. [75]

    Li, J.-C

    X. Li, J.-C. Huang, G.-Z. Zhang, H.-E. Li, Z.-P. Shen, C. Zhao, J. Li, and H.-S. Hu, The Journal of Chemical Physics160, 234102 (2024)

    2024

  76. [76]

    Wang, H.-Q

    J.-Q. Wang, H.-Q. Wu, R.-Q. He, and Z.-Y. Lu, Physical Review B109, 245120 (2024)

    2024

  77. [77]

    J. Nys, Z. Denis, and G. Carleo, Physical Review B109, 235120 (2024)

    2024

  78. [78]

    W. T. Lou, H. Sutterud, G. Cassella, W. Foulkes, J. Knolle, D. Pfau, and J. S. Spencer, Physical Review X 14, 021030 (2024)

    2024

  79. [79]

    S. Lu, G. Giudice, and J. I. Cirac, Physical Review B 111, 075102 (2025)

    2025

  80. [80]

    W.-L. Wu, L. Meng, and S.-L. Zhu, Physical Review Let- ters136, 071901 (2026)

    2026

Showing first 80 references.