Pith. sign in

REVIEW 3 major objections 4 minor 132 references

A variational Monte Carlo construction treats the full, continuous SU(2) lattice gauge theory with dynamical fermions, without a sign problem, and satisfies Gauss's law to machine precision.

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 00:44 UTC pith:VIKO4RCJ

load-bearing objection A genuine variational first for continuous SU(2) with dynamical fermions, but validated only where the ansatz is nearly trivial; the physical claims are preliminary. the 3 major comments →

arxiv 2607.26131 v1 pith:VIKO4RCJ submitted 2026-07-28 hep-lat cond-mat.quant-gascond-mat.str-elhep-phquant-ph

Neural quantum states for non-Abelian lattice gauge theories with dynamical fermions

Gabriel Rouxinol , Julian Bender , Michele Grossi , Patrick Emonts , Jad C. Halimeh This is my paper
classification hep-lat cond-mat.quant-gascond-mat.str-elhep-phquant-ph
keywords neural quantum stateslattice gauge theorySU(2) gauge theorydynamical staggered fermionsvariational Monte CarloGauss's lawsign problemstrong-coupling perturbation theory
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.

This paper claims to construct the first sign-problem-free variational Monte Carlo ground state for the untruncated, fully continuous SU(2) lattice gauge theory coupled to dynamical staggered fermions on a two-dimensional square lattice. The central construction couples a neural-network gauge wavefunction sampled in the magnetic basis to a gauge-covariant Gaussian fermionic correction built from the eigenvectors of the mass–hopping Hamiltonian and short Wilson lines. For every sampled gauge configuration the fermionic part is a Gaussian state, which yields exact analytic formulas for all fermionic energy contributions, yet after integrating out the gauge fields the full matter state is a superposition of Gaussians and can capture non-Gaussian correlations. The paper validates the ansatz against strong-coupling perturbation theory, reports machine-precision Gauss-law satisfaction, uses hysteresis between two initializations to locate a magnetic transition near λ*≈−0.04, and along λ=4/g² finds states increasingly far from the reference Néel state as L grows or g² shrinks.

Core claim

The central claim is that the combined state |Ψ⟩ = ∫DU ΨG(U) Ûcorr(U)|ΨN⟩|U⟩ is a sign-problem-free, gauge-invariant variational representation of the ground state of the 2+1D SU(2) lattice gauge theory with staggered fermions, with no truncation of the gauge group. The generator H_full(U) equals V_occ A(U) V_unocc† + H.c., where V_occ and V_unocc are the low- and high-energy eigenvector blocks of the mass–hopping matrix h_MH(U), and A(U) is a sum over three Hermitian Wilson aggregates (distance-1, straight distance-2, and diagonal distance-2 paths) with coefficients constant on twofold-degenerate pair blocks. Because the fermionic correction is Gaussian at fixed U, the occupation matrix P(U

What carries the argument

The load-bearing object is the gauge-covariant Gaussian fermionic rotation Ûcorr(U)=exp(i∑ψ†[H_full(U)]ψ), whose matrix U_corr(U)=e^{iH_full(U)} acts on the fixed gauge-invariant Néel reference projector P_N. H_full is assembled from eigenvectors of the mass–hopping Hamiltonian h_MH(U)=h_m−(it/2)h_g(U) and from Hermitian Wilson aggregates W_{d1}, W_{d2s}, and W_{d2d} built from length-1 and length-2 paths; a pseudoreality symmetry forces the eigenvectors into twofold-degenerate pairs, and the variational coefficients are chosen constant on each pair block, eliminating basis ambiguity and keeping the parameter count polynomial in system size. This mechanism ensures the fermionic occupation ma

Load-bearing premise

The load-bearing premise is that a fixed Néel reference state plus a Gaussian fermionic rotation whose generator is cut off at Wilson lines of length two is expressive enough to represent the true ground state at intermediate couplings, where no external benchmark exists.

What would settle it

At an intermediate coupling, say g²≈0.632 along λ=4/g², extend the Wilson-line cutoff in the fermionic generator from distance 2 to distance 3 or 4 and compare the variational energy per site; if the energy changes by more than the Monte Carlo error, or the hysteresis-based transition point shifts by more than the scan resolution, the length-2 truncation is too restrictive and the claimed ground-state approximation fails at those couplings.

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

If this is right

  • The full continuous SU(2) group can be included without truncating the electric-field Hilbert space, so variational energies and plaquette averages are free of the gauge-truncation systematic that limits quantum-simulation and tensor-network studies.
  • All fermionic contributions to the energy and to the training gradients are known analytically for each sampled configuration, so the Monte Carlo cost stays polynomial and sign-problem-free even though the matter state after integrating out gauge fields is non-Gaussian.
  • In the strong-coupling limit the variational energies agree with the effective antiferromagnetic spin-model prediction within errors (0.02%–1.5% on the benchmark points), validating the ansatz where exact perturbation theory exists.
  • A two-initialization hysteresis scan of ⟨cos Bp⟩ on L=4 and L=6 lattices indicates a magnetic ordering transition near λ*≈−0.04, showing that initialization dependence can be used as a phase-transition diagnostic, with the transition point consistent between the two system sizes within resolution.
  • Along the physical line λ=4/g², the relative energy variance for L=8 stays in the 0.01–0.1 range, which the paper reads as evidence that the state approximates the ground state, and smaller g² and larger L drive the fermions away from the Néel reference.

Where Pith is reading between the lines

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

  • The length-2 cutoff in the Wilson aggregates of the fermionic generator is the least controlled element of the construction; extending it to length 3–4 at intermediate couplings is the direct experiment that would confirm or break the approach.
  • Because the transition at λ*≈−0.04 is inferred from hysteresis between two variational minima, its precise location remains approximate; a finite-size scaling study of an unbiased order parameter would be the next step before firm conclusions about the phase diagram.
  • The pseudoreality argument is specific to the fundamental representation of SU(2), so transferring the construction to SU(3) will require redesigning the covariance blocks, not just re-running the same ansatz.
  • If the sign-problem-free property is robust, the same variational states could be reused to estimate Wilson-loop area laws and the Fredenhagen–Marcu order parameter with only denser (λ,g²) scans, pointing the way toward a sharper confinement characterization.

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

3 major / 4 minor

Summary. The manuscript proposes a variational Monte Carlo framework for the untruncated, fully continuous SU(2) lattice gauge theory in 2+1D coupled to dynamical staggered fermions. The total state is a coherent superposition |Ψ⟩ = ∫DU Ψ_G(U) Û_corr(U)|Ψ_N⟩|U⟩, where Ψ_G(U) is a neural-network/Jastrow gauge wavefunction in the magnetic basis and Û_corr(U) is a gauge-covariant Gaussian fermionic correction generated by a one-body Hermitian operator built from eigenvectors of the mass-hopping Hamiltonian and Wilson lines of length at most 2. The paper derives analytical estimators for all fermionic contributions to the energy, verifies Gauss's law to machine precision, benchmarks against strong-coupling perturbation theory (Table I), and presents a coarse (g², λ) phase diagram with a hysteresis-like transition near λ* ≈ −0.04. It claims to be the first sign-problem-free variational treatment covering the full continuous non-Abelian, matter-coupled regime.

Significance. If the method delivers what is claimed, it is a useful step toward variational studies of non-Abelian lattice gauge theories with dynamical matter. The construction is explicit and has real strengths: the covariance argument (Sec. III B) is carefully organized; the analytical expectation-value formulas (Sec. IV, App. A) are nontrivial and reduce the computational cost; the parameter count is polynomial (Eq. (24)); and the strong-coupling benchmark in Table I agrees with a parameter-free Schrieffer-Wolff expansion to 0.02–1.5%. These are concrete, reproducible contributions. However, the physical conclusions—especially the phase diagram and the claim of a good ground-state approximation at intermediate couplings—rest on variational expressivity that is only weakly tested in the regime where those conclusions are drawn. The manuscript itself states that the effect of increasing the Wilson-line truncation length is left to future work (Sec. III A).

major comments (3)
  1. [§VI A, Table I; §VI C, Fig. 8] The only external quantitative validation is at g²=20, deep in the strong-coupling regime where the correction to the Néel reference is small. Table I therefore does not constrain the ansatz at intermediate couplings, e.g. g²≈0.5–2 and λ≈−0.04, where the phase diagram and the physical-line results are reported. The relative variance σ_r²≈0.01–0.1 shown in Fig. 8 is by itself a weak certificate: a restricted variational family can have small energy variance while being far from the true ground state. The central claim that the state is a good approximation of the ground state in the regime of physical interest needs a benchmark at moderate coupling—for example, comparison with exact diagonalization on a small lattice, with tensor networks, or at minimum a systematic study of the Wilson-line truncation length.
  2. [§VI B, Figs. 4–5] The phase transition at λ* ≈ −0.04 is inferred from two different local minima obtained with two different initializations ('hysteresis'). This is not a hysteresis loop and, more importantly, distinct variational local minima can be produced by the restricted Gaussian ansatz or by the optimization protocol rather than by a genuine ground-state phase transition. No energy crossing, finite-size scaling of the order parameter, or histogram/overlap diagnostic is provided. The claimed transition location also has no uncertainty estimate and the λ grid spacing (0.05) is comparable to the reported value. The paper should either provide stronger evidence for a true transition or explicitly present this as a variational metastability study, not as a determination of the phase boundary.
  3. [§III A, Eq. (12)] The fermionic generator is restricted to Wilson lines of length at most 2. As the text states, longer Wilson lines are generated by exponentiation, but their coefficients are not independent variational parameters; they are determined by the nine short-distance channels. This truncation is unchecked in the regime where the physical conclusions are drawn. Since the ansatz's expressivity is the load-bearing premise for the phase diagram and the ground-state approximation claims, the manuscript needs either a truncation-length convergence study or a direct benchmark at intermediate coupling. Without this, the stated limitation in Sec. III A is not a peripheral caveat but a central gap in the evidence.
minor comments (4)
  1. [Fig. 8] The horizontal axis labels appear as '10□1' and '10□1' (likely superscript rendering artifacts); please fix the axis to read 10⁻¹, 10⁰, 10¹.
  2. [Sec. VII] The phrase 'first sign-problem-free variational treatment' is a strong priority claim. It may be correct, but it should be stated more carefully, since sign-problem freedom here refers to the Monte Carlo sampler with weights |Ψ_G(U)|² and the Gaussian fermionic estimators; the precise sense should be spelled out to avoid ambiguity.
  3. [Eq. (24)] The parameter count is stated as 9/2 L⁴ real parameters, but no account is taken of possible redundancies from global symmetries; the text acknowledges this. It would be helpful to state explicitly whether the reported count is an upper bound.
  4. [Sec. V] The distinction between the 'matter warm-up' phase and the main matter-training rounds is clear, but the number of matter steps per cycle (n_ms=15, n_ss=10) and the 128-sample diagnostics are only described for one representative run; a short table of all hyperparameters used for the phase-diagram runs would improve reproducibility.

Circularity Check

0 steps flagged

No circular reduction: the core derivation is self-contained; at most a minor non-load-bearing self-citation.

full rationale

The derivation chain is not circular. The variational state Eq. (25) is an ansatz: a gauge-invariant gauge wavefunction multiplied by a gauge-covariant Gaussian fermionic correction. Gauge covariance of the correction is proven by construction in Eqs. (17)-(23), and the Fig. 1 Gauss-law diagnostic is explicitly labeled as a numerical consistency check, not a prediction. The strong-coupling benchmark (Table I) is computed against the Schrieffer-Wolff effective Hamiltonian Eq. (32), which is parameter-free, derived in App. C with stated assumptions, and matched to the known external result Ref. [134]; the variational energies are not fitted to ePT, so the benchmark is independent support. The path-length-2 truncation in Sec. III A is an acknowledged expressivity limitation ('The analysis on how increasing the truncation length affects the quality of the obtained results is left as future work'), but it is not a circular reduction: the predicted energies and phase diagram are outputs of optimization, not definitions in terms of fitted parameters. The only self-citations are the companion Letter [123] (forward reference, not load-bearing) and the U(1) Gaussian-ansatz method [119] (shared co-authors, but a published, transferred method whose analytical formulas are re-derived here in Sec. IV and App. A). No uniqueness theorem from the authors' own work is invoked to force the ansatz. Therefore the central claims do not reduce to their inputs by construction; the main risk is variational expressivity at intermediate coupling, which is a correctness/limitation concern rather than circularity.

Axiom & Free-Parameter Ledger

5 free parameters · 6 axioms · 0 invented entities

No new physical entities (particles, forces, dimensions, symmetries) are postulated. The new objects — the gauge-covariant Gaussian correction Ûcorr(U), the Wilson aggregates W_{d1}, W_{d2s}, W_{d2d}, and the Kramers-pair scalar blocks — are variational constructions whose adequacy, not existence, is at issue. Free parameters are dominated by the variational coefficients themselves, the truncation choice, and the read-off phase boundary; the protocol hyperparameters are hand-chosen and materially affect the L=8 claims.

free parameters (5)
  • Matter ansatz block coefficients C^(1)_d, C^(oo)_d, C^(uu)_d = 9 channels × (L²/2)² 2×2-scalar blocks → (9/4)L⁴ complex parameters at half filling; optimized by energy minimization
    These variational parameters determine the Gaussian fermionic correction; every physics result (Table I, Figs. 2–9) depends on the optimizer finding good values, and at intermediate coupling there is no independent check of their sufficiency.
  • Gauge wavefunction parameters (Jastrow two-body term + CNN weights) = Borrowed from Ref. [118]; α set to large positive/negative values for the ±⟨cos Bp⟩ initializations at g²=0
    Borrowed wholesale from the pure-gauge method [118]; the phase-diagram scans (Figs. 4–5) are seeded with these parameters, so the hysteresis pattern inherits the gauge ansatz's variational quality.
  • Wilson-line truncation length = 2 (path types: d1, d2s, d2d)
    A modeling choice restricting the generator to short Wilson lines (Sec. III A); its adequacy is explicitly unexamined ('left as future work').
  • Phase boundary λ* = ≈ −0.04 (no error bars)
    Read from the coarse (g², λ) grid; the two initializations disagree over a wide band λ∈[−0.15, 0.05], and consistency between L=4 and L=6 is claimed only 'within our resolution'.
  • Training protocol (n_pg, n_pm, n_cycles, n_ms, n_ss, n_gs, batch sizes, learning rates) = n_cycles=80/30/5 for L=4/6/8; gauge lr 10⁻³→3×10⁻⁴; matter AdamW lr 5×10⁻⁴×0.1^{c/(n_cycles−1)}; 1024 samples, 64 chains
    Hand-set; the L=8 convergence claim rests on n_cycles=5 after warm transfer from smaller lattices.
axioms (6)
  • standard math Pseudoreality of the SU(2) fundamental representation gives T=(S⊗iσ₂)K with T²=−1, hence Kramers-degenerate pairs for hMH(U)
    Sec. III A, Eq. (6). Underlies the block structure used in the covariance proof; without the pair structure the coefficient parametrization is not gauge-covariant.
  • domain assumption The occupied/unoccupied eigenspaces of hMH(U) are separated by a gap for all sampled U, so Vocc/Vunocc are smooth and differentiable
    Sec. III A–B; needed for the covariance proof (Eqs. 19–22) and for the derivative estimators f^ξ (App. A). Level crossings would make the ansatz discontinuous; not verified numerically.
  • standard math The strong-coupling (Schrieffer-Wolff) expansion truncated at second order provides the benchmark energy
    App. C, Eq. (32). Standard technique, matched to the known result of Ref. [134]; agreement to ≤1.5% is the paper's main quantitative validation.
  • domain assumption The gauge wavefunction ΨG from Ref. [118] remains an accurate variational component when coupled to matter
    Borrowed without modification (Sec. III); the coupled-state quality is not independently checked in the intermediate-coupling regime.
  • ad hoc to paper The length-2 Wilson-line truncation of the fermionic generator is adequate at the couplings studied
    Sec. III A: 'Restricting the construction to a path length of at most 2 is the truncation used in this work... left as future work.' This is the strongest unvalidated modeling choice.
  • domain assumption The inference from variational hysteresis (two local minima) to the existence of a genuine phase transition
    Sec. VI B; the authors note the two minima could reflect optimization trapping and defer the physical study to the companion Letter [123].

pith-pipeline@v1.3.0-alltime-deepseek · 5575 in / 14521 out tokens · 397799 ms · 2026-08-01T00:44:37.340965+00:00 · methodology

0 comments
read the original abstract

Determining the ground state of non-Abelian lattice gauge theories coupled to dynamical fermions is key to understanding confinement and the phase structure of gauge--matter systems. We present a variational Monte Carlo framework for the ground state of the untruncated fully-continuous SU$(2)$ lattice gauge theory coupled to dynamical staggered fermions on an $L\times L$ square lattice. We work in the magnetic basis with a neural-network representation of the gauge wavefunction. The fermions are described by a gauge-covariant Gaussian fermionic correction built on a fixed N\'eel reference state where, for each sampled gauge configuration $\mathbf{U}$, the correction is generated by a Hermitian operator. This operator is constructed from short Wilson lines and the eigenvectors of the mass--hopping Hamiltonian, with number of variational parameters polynomial in the system size. This Gaussian structure also gives analytical expressions for all fermionic contributions to the energy and related observables in terms of the fermion occupation matrix. The results are validated against strong-coupling perturbation theory, where they recover the expected effective antiferromagnetic spin Hamiltonian. Using this framework, we map a coarse ground state phase diagram in the plane of independent electric and magnetic couplings $(g^2, \lambda)$ and show that a hysteresis analysis can identify the existence of phase transitions. Restoring the physical relation $\lambda=4/g^2$, we characterize how increasing the system size and changing the electric coupling $g^2$ move the state away from the reference N\'eel state, for lattice sizes $L=4,6,8$. More broadly, the method offers a sign-problem-free variational framework for continuous non-Abelian gauge groups with dynamical matter that should extend to other matter content and higher-dimensional lattices.

Figures

Figures reproduced from arXiv: 2607.26131 by Gabriel Rouxinol, Jad C. Halimeh, Julian Bender, Michele Grossi, Patrick Emonts.

Figure 1
Figure 1. Figure 1: FIG. 1. Gauss-law diagnostic [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Spatial profile of the optimized state for the same 4 [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Cycle-by-cycle evolution of the energy contributions [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Color maps of the plaquette observable [PITH_FULL_IMAGE:figures/full_fig_p009_4.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Spatial profile of the optimized state for the 4 [PITH_FULL_IMAGE:figures/full_fig_p010_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Training of the total energy of the system as the [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. Evolution of the relative variance [PITH_FULL_IMAGE:figures/full_fig_p011_8.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

132 extracted references · 17 linked inside Pith

  1. [1]

    Weinberg,The Quantum Theory of Fields(Cam- bridge University Press, 1995)

    S. Weinberg,The Quantum Theory of Fields(Cam- bridge University Press, 1995)

    1995

  2. [2]

    Weinberg, Eur

    S. Weinberg, Eur. Phys. J. C34, 5 (2004), arXiv:hep- ph/0401010

    arXiv 2004

  3. [3]

    Peskin and D

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

    2018

  4. [4]

    Schwartz,Quantum Field Theory and the Standard Model(Cambridge University Press, 2014)

    M. Schwartz,Quantum Field Theory and the Standard Model(Cambridge University Press, 2014)

    2014

  5. [5]

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

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

    2007

  6. [6]

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

    1973

  7. [7]

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

    1974

  8. [8]

    Kogut and L

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

    1975

  9. [9]

    Baskaran, Z

    G. Baskaran, Z. Zou, and P. W. Anderson, Solid State Communications63, 973 (1987)

    1987

  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]

    Creutz, L

    M. Creutz, L. Jacobs, and C. Rebbi, Physical Review D 20, 1915 (1979)

    1915

  14. [14]

    Carlson, Reviews of Modern Physics87, 1067 (2015)

    J. Carlson, Reviews of Modern Physics87, 1067 (2015)

    2015

  15. [15]

    C. R. Allton, M. Ciuchini, M. Crisafulli, E. Franco, V. Lubicz, and G. Martinelli, Nuclear Physics B431, 667 (1994)

    1994

  16. [16]

    Fodor and S

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

    2002

  17. [17]

    Troyer and U.-J

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

    2005

  18. [18]

    Vicari and H

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

    2009

  19. [19]

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

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

    2007

  20. [20]

    Boyda and others, inSnowmass 2021(2022) eprint: 2202.05838

    D. Boyda and others, inSnowmass 2021(2022) eprint: 2202.05838

    Pith/arXiv arXiv 2021

  21. [21]

    Alexandru, G

    A. Alexandru, G. Ba¸ sar, P. F. Bedaque, and N. C. War- rington, Reviews of Modern Physics94, 015006 (2022)

    2022

  22. [22]

    Kanwar, Physical Review Letters125, 10.1103/PhysRevLett.125.121601 (2020)

    G. Kanwar, Physical Review Letters125, 10.1103/PhysRevLett.125.121601 (2020)

    doi:10.1103/physrevlett.125.121601 2020

  23. [24]

    Lawrence and Y

    S. Lawrence and Y. Yamauchi, Physical Review D103, 114509 (2021)

    2021

  24. [26]

    Hisayoshi, K

    K. Hisayoshi, K. Kashiwa, Y. Namekawa, and H. Takase, Physical Review D111, 094503 (2025)

    2025

  25. [27]

    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

  26. [28]

    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

  27. [29]

    Byrnes and Y

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

    2006

  28. [30]

    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

  29. [31]

    Dalmonte and S

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

    arXiv 2016

  30. [32]

    Aidelsburger, L

    M. Aidelsburger, L. Barbiero, A. Bermudez, T. Chanda, A. Dauphin, D. Gonz´ alez-Cuadra, P. R. Grzy- bowski, 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. Za- krzewski, E. Zohar, and M. Lewenstein, Philosophi- cal Transactions of the Royal Society ...

    2021

  31. [33]

    Zohar, J

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

    2015

  32. [34]

    Barata, X

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

    2022

  33. [35]

    Barata, X

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

    2023

  34. [36]

    Barata, W

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

    2024

  35. [37]

    J. C. Halimeh, M. V. Damme, T. V. Zache, D. Banerjee, and P. Hauke, Quantum6, 878 (2022)

    2022

  36. [38]

    J. C. Halimeh, I. P. McCulloch, B. Yang, and P. Hauke, PRX Quantum3, 040316 (2022)

    2022

  37. [39]

    N. Klco, E. F. Dumitrescu, A. J. McCaskey, T. D. Mor- ris, R. C. Pooser, M. Sanz, E. Solano, P. Lougovski, and M. J. Savage, Physical Review A98, 032331 (2018)

    2018

  38. [40]

    Zhang, Y

    W.-Y. Zhang, Y. Liu, Y. Cheng, M.-G. He, H.-Y. Wang, T.-Y. Wang, Z.-H. Zhu, G.-X. Su, Z.-Y. Zhou, Y.-G. Zheng, H. Sun, B. Yang, P. Hauke, W. Zheng, J. C. Halimeh, Z.-S. Yuan, and J.-W. Pan, Nature Physics 21, 155 (2025)

    2025

  39. [41]

    R. C. Farrell, M. Illa, A. N. Ciavarella, and M. J. Savage, PRX Quantum5, 020315 (2024)

    2024

  40. [42]

    R. C. Farrell, I. A. Chernyshev, S. J. Powell, N. A. Zem- levskiy, M. Illa, and M. J. Savage, Physical Review D 107, 054513 (2023)

    2023

  41. [43]

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

    2021

  42. [44]

    A. T. Than, Y. Y. Atas, A. Chakraborty, J. Zhang, M. T. Diaz, K. Wen, X. Liu, R. Lewis, A. M. Green, C. A. Muschik, and N. M. Linke, Nature Communica- tions16, 10288 (2025)

    2025

  43. [45]

    Angelides, P

    T. Angelides, P. Naredi, A. Crippa, K. Jansen, S. K¨ uhn, I. Tavernelli, and D. S. Wang, npj Quantum Information 11, 6 (2025)

    2025

  44. [46]

    Schuhmacher, G.-X

    J. Schuhmacher, G.-X. Su, J. J. Osborne, A. Gandon, J. C. Halimeh, and I. Tavernelli, Observation of hadron scattering in a lattice gauge theory on a quantum com- puter (2025), arXiv:2505.20387 [quant-ph]

    Pith/arXiv arXiv 2025

  45. [47]

    Davoudi, C.-C

    Z. Davoudi, C.-C. Hsieh, and S. V. Kadam, Quantum computation of hadron scattering in a lattice gauge the- ory (2025), arXiv:2505.20408 [quant-ph]

    Pith/arXiv arXiv 2025

  46. [48]

    Z. Li, M. Illa, and M. J. Savage, A Framework for Quan- tum Simulations of Energy-Loss and Hadronization in Non-Abelian Gauge Theories: SU(2) Lattice Gauge Theory in 1+1D (2026), arXiv:2512.05210 [quant-ph]

    Pith/arXiv arXiv 2026

  47. [49]

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

    2020

  48. [50]

    Desaules, A

    J.-Y. Desaules, A. Hudomal, D. Banerjee, A. Sen, Z. Papi´ c, and J. C. Halimeh, Physical Review B107, 205112 (2023)

    2023

  49. [51]

    Schweizer, F

    C. Schweizer, F. Grusdt, M. Berngruber, L. Barbiero, E. Demler, N. Goldman, I. Bloch, and M. Aidelsburger, Nature Physics15, 1168 (2019)

    2019

  50. [52]

    G.-X. Su, H. Sun, A. Hudomal, J.-Y. Desaules, Z.-Y. Zhou, B. Yang, J. C. Halimeh, Z.-S. Yuan, Z. Papi´ c, and J.-W. Pan, Physical Review Research5, 023010 (2023)

    2023

  51. [53]

    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

  52. [54]

    Ciavarella, N

    A. Ciavarella, N. Klco, and M. J. Savage, Physical Re- view D103, 094501 (2021)

    2021

  53. [55]

    A. N. Ciavarella, Physical Review D108, 10.1103/Phys- RevD.108.094513 (2023)

    doi:10.1103/phys- 2023

  54. [56]

    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

  55. [57]

    Tagliacozzo, A

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

    2013

  56. [58]

    A. Kan, L. Funcke, S. K¨ uhn, L. Dellantonio, J. Zhang, J. F. Haase, C. A. Muschik, and K. Jansen, PoSLA T- TICE2021, 112 (2022), eprint: 2111.02238

    Pith/arXiv arXiv 2022

  57. [59]

    Magnifico, T

    G. Magnifico, T. Felser, P. Silvi, and S. Montangero, Nature Communications12, 3600 (2021)

    2021

  58. [60]

    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

  59. [61]

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

    2025

  60. [62]

    Turro, A

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

    2024

  61. [63]

    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

  62. [64]

    Mildenberger, W

    J. Mildenberger, W. Mruczkiewicz, J. C. Halimeh, Z. Jiang, and P. Hauke, Nature Physics21, 312 (2025)

    2025

  63. [65]

    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

  64. [66]

    Crippa, K

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

    Pith/arXiv arXiv 2024

  65. [67]

    A. N. Ciavarella, S. Hariprakash, J. C. Halimeh, and C. W. Bauer, Truncation uncertainties for accurate quantum simulations of lattice gauge theories (2026), arXiv:2508.00061 [quant-ph]

    Pith/arXiv arXiv 2026

  66. [68]

    Ebner, A

    L. Ebner, A. Sch¨ afer, C. Seidl, B. M¨ uller, and X. Yao, Physical Review D110, 014505 (2024)

    2024

  67. [69]

    G. D. Paciani, L. Homeier, J. C. Halimeh, M. Aidels- burger, and F. Grusdt, Quantum simulation of fermionic non-Abelian lattice gauge theories in (2+1)D with built- in gauge protection (2025), arXiv:2506.14747 [cond- mat.quant-gas]

    Pith/arXiv arXiv 2025

  68. [70]

    Joshi, Y

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

    Pith/arXiv arXiv 2026

  69. [71]

    K. Xu, U. Borla, K. Hemery, R. Joshi, H. Dreyer, E. Rinaldi, and J. C. Halimeh, Observation of glue- ball excitations and string breaking in a 2 + 1DZ 2 lat- tice gauge theory on a trapped-ion quantum computer (2026), arXiv:2604.07435 [hep-lat]

    Pith/arXiv arXiv 2026

  70. [72]

    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

  71. [73]

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

    2022

  72. [74]

    S. R. White, Physical Review Letters69, 2863 (1992)

    1992

  73. [75]

    S. R. White, Physical Review B48, 10345 (1993)

    1993

  74. [76]

    Schollw¨ ock, Annals of Physics January 2011 Special Issue,326, 96 (2011)

    U. Schollw¨ ock, Annals of Physics January 2011 Special Issue,326, 96 (2011)

    2011

  75. [77]

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

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

    2014

  76. [78]

    Montangero,Introduction to Tensor Network Meth- ods: Numerical simulations of low-dimensional many- body quantum systems(Springer International Publish- ing, Cham, 2018)

    S. Montangero,Introduction to Tensor Network Meth- ods: Numerical simulations of low-dimensional many- body quantum systems(Springer International Publish- ing, Cham, 2018)

    2018

  77. [79]

    Ba˜ nuls, K

    M. Ba˜ nuls, K. Cichy, J. Cirac, and K. Jansen, Journal of High Energy Physics2013, 158 (2013)

    2013

  78. [80]

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

    2017

  79. [81]

    Belyansky, S

    R. Belyansky, S. Whitsitt, N. Mueller, A. Fahimniya, E. R. Bennewitz, Z. Davoudi, and A. V. Gorshkov, Physical Review Letters132, 091903 (2024)

    2024

  80. [82]

    Rouxinol, T

    G. Rouxinol, T. Magorsch, J. J. Osborne, N. Brambilla, and J. C. Halimeh, Schwinger Model with a Dynamical Axion (2026), arXiv:2603.12194 [hep-ph]

    arXiv 2026

Showing first 80 references.