arxiv: 2604.06716 · v1 · submitted 2026-04-08 · ✦ hep-lat · hep-ph· nucl-th· quant-ph

Recognition: 1 theorem link

· Lean Theorem

Quantum simulation of baryon scattering in SU(2) lattice gauge theory

Jo\~ao Barata , Juan Hormaza , Zhong-Bo Kang , Wenyang Qian

Authors on Pith no claims yet

Pith reviewed 2026-05-10 18:25 UTC · model grok-4.3

classification ✦ hep-lat hep-phnucl-thquant-ph

keywords SU(2) lattice gauge theorybaryon scatteringquantum simulationtensor networksentanglementmeson-baryon collisionsreal-time dynamicshadronic processes

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The pith

In SU(2) lattice gauge theory, meson-baryon scattering produces entanglement that delocalizes the slower particle while the faster one moves ballistically.

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

The paper simulates real-time scattering of mesons and baryons in a one-dimensional SU(2) lattice gauge theory with fundamental fermions. It examines processes in sectors of fixed baryon number B equal to zero, one, or two, which correspond to meson-meson, meson-baryon, and baryon-baryon collisions. At strong coupling the pure meson and pure baryon sectors follow mostly elastic rules that match the simpler Schwinger model. The mixed sector instead generates quantum entanglement between the colliding wave packets. This causes the slower particle to spread out in space while the faster particle continues its straight-line motion.

Core claim

At strong coupling, the B=0 and B=2 channels exhibit predominantly elastic dynamics closely resembling the U(1) Schwinger model. The mixed B=1 sector displays qualitatively new behavior: meson and baryon wavepackets become entangled during the collision, with the slower state becoming spatially delocalized while the faster one propagates ballistically. These processes are characterized through local observables, entanglement entropy, and the information lattice.

What carries the argument

Tensor-network methods applied to the gaugeless Hamiltonian in fixed-baryon-number sectors, tracking real-time wave-packet evolution and entanglement measures.

Load-bearing premise

The tensor-network truncation and gaugeless Hamiltonian formulation reproduce the continuum dynamics of the full SU(2) theory without introducing uncontrolled artifacts in the scattering observables.

What would settle it

A higher-precision simulation with increased bond dimension or restored gauge degrees of freedom that shows no delocalization or entanglement in the B=1 sector would falsify the reported new behavior.

Figures

Figures reproduced from arXiv: 2604.06716 by Jo\~ao Barata, Juan Hormaza, Wenyang Qian, Zhong-Bo Kang.

read the original abstract

We present a first real-time study of hadronic scattering in a $(1+1)$-dimensional SU(2) lattice gauge theory with fundamental fermions using tensor-network techniques. Working in the gaugeless Hamiltonian formulation, we investigate scattering processes across sectors of fixed global baryon number $B = 0, 1, 2$, corresponding respectively to meson--meson, meson--baryon, and baryon--baryon collisions. At strong coupling, the $B = 0$ and $B = 2$ channels exhibit predominantly elastic dynamics closely resembling the U(1) Schwinger model. The mixed $B = 1$ sector displays qualitatively new behavior: meson and baryon wavepackets become entangled during the collision, with the slower state becoming spatially delocalized while the faster one propagates ballistically. We characterize these processes through local observables, entanglement entropy, and the information lattice.

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 is the first tensor-network simulation of real-time baryon scattering in SU(2) with fermions, showing mostly elastic behavior in B=0 and B=2 but new delocalization in B=1.

read the letter

The paper gives the first real-time tensor-network results for meson-baryon and baryon-baryon scattering in a non-Abelian lattice gauge theory. It works in the gaugeless formulation of SU(2) with fundamental fermions and evolves wave packets in fixed baryon-number sectors. At strong coupling the B=0 and B=2 channels look elastic and close to the Schwinger model, while the B=1 channel shows the meson and baryon states entangling, with the slower one spreading out spatially. They track this with local densities, entanglement entropy, and the information lattice. That is the concrete advance over prior U(1) work. The numerics appear direct and parameter-free, which is a plus. The main soft spot is whether the delocalization in the mixed sector is physical or an artifact of finite bond dimension. The abstract gives no bond-dimension scaling, error bars, or lattice-spacing checks, so the new behavior rests on the assumption that the MPS truncation faithfully captures the long-range entanglement. The fact that the same setup reproduces the known U(1)-like results in the other sectors is helpful but does not test the B=1 claim. A reader who already works on tensor networks for gauge theories will find the setup and observables useful. The work is still at the stage where more convergence data would strengthen it, but the question it asks is well-posed and the method is reproducible in principle. I would send it to peer review so the authors can address the truncation checks.

Referee Report

1 major / 0 minor

Summary. The manuscript presents the first real-time tensor-network simulation of hadronic scattering in (1+1)-dimensional SU(2) lattice gauge theory with fundamental fermions, using the gaugeless Hamiltonian formulation. It examines scattering in fixed baryon-number sectors B=0 (meson-meson), B=1 (meson-baryon), and B=2 (baryon-baryon) at strong coupling. The B=0 and B=2 channels are reported to exhibit predominantly elastic dynamics resembling the U(1) Schwinger model, while the B=1 sector shows qualitatively new behavior: entanglement of meson and baryon wavepackets during collision, with the slower state becoming spatially delocalized and the faster one propagating ballistically. These processes are characterized via local observables, entanglement entropy, and the information lattice.

Significance. If the results are robust against numerical artifacts, this constitutes a significant advance in applying tensor networks to real-time non-Abelian gauge dynamics, providing qualitative insights into baryon scattering beyond exactly solvable Abelian models. The direct numerical evolution without fitted parameters and the cross-check against the Schwinger model in the B=0 and B=2 sectors are strengths that support the methodological contribution.

major comments (1)

[Abstract and B=1 sector results] Abstract and B=1 sector results: The central claim of qualitatively new behavior in the B=1 channel (entanglement during collision and spatial delocalization of the slower state) rests on the tensor-network simulation faithfully capturing the physics. No convergence tests with bond dimension, lattice spacing, or truncation error estimates are described for the key observables in this sector. In the gaugeless formulation, the constrained fermion Hilbert space combined with finite-bond-dimension MPS/TTN truncation can artificially induce or suppress long-range entanglement, potentially causing the reported delocalization as a numerical artifact. This is load-bearing because the B=0 and B=2 sectors match the Schwinger model but provide no independent cross-check for the mixed B=1 dynamics.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript, the positive assessment of its significance, and the recommendation for major revision. We address the concerns about convergence and potential numerical artifacts in the B=1 sector below. We will revise the manuscript to incorporate additional numerical details and tests.

read point-by-point responses

Referee: No convergence tests with bond dimension, lattice spacing, or truncation error estimates are described for the key observables in this sector.

Authors: We agree that the original manuscript does not provide sufficient detail on these convergence aspects for the B=1 sector. In the revised version we will add a new subsection (or appendix) presenting bond-dimension scaling for the local observables, entanglement entropy, and information lattice in the B=1 channel. We will also report the truncation error thresholds used during time evolution and briefly discuss finite-volume and lattice-spacing considerations at the fixed strong-coupling value employed. revision: yes
Referee: In the gaugeless formulation, the constrained fermion Hilbert space combined with finite-bond-dimension MPS/TTN truncation can artificially induce or suppress long-range entanglement, potentially causing the reported delocalization as a numerical artifact. This is load-bearing because the B=0 and B=2 sectors match the Schwinger model but provide no independent cross-check for the mixed B=1 dynamics.

Authors: We agree that finite bond dimension can in principle limit entanglement, but we do not believe the observed delocalization is an artifact. The gaugeless formulation exactly enforces the gauge constraints by construction, working entirely within the physical subspace; no additional gauge-fixing approximations are introduced. The delocalization of the slower wave packet is directly correlated with the dynamical growth of entanglement entropy between the meson and baryon, a feature absent in the Abelian Schwinger model and arising from the SU(2) color structure. The B=0 and B=2 results validate the overall implementation and time-evolution algorithm for elastic processes, while the B=1 channel constitutes a genuine prediction of the non-Abelian theory. To address the concern, the revision will include explicit comparisons at multiple bond dimensions for the B=1 observables, demonstrating that the qualitative delocalization and entanglement features remain stable above a threshold bond dimension. revision: partial

Circularity Check

0 steps flagged

No significant circularity; results from direct numerical evolution

full rationale

The paper reports outcomes from real-time tensor-network evolution of initial wavepackets in a gaugeless SU(2) Hamiltonian on a lattice. No parameters are fitted to the target scattering observables, no self-referential definitions equate inputs to outputs, and no uniqueness theorems or ansatzes from prior self-citations are invoked to force the reported entanglement or delocalization patterns. The B=0 and B=2 sectors are compared to the known Schwinger model for validation, but the B=1 results stand as independent simulation data without reduction to the input state by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The simulation rests on standard lattice gauge theory assumptions plus the validity of the gaugeless formulation and tensor-network truncation; no new entities are postulated.

axioms (2)

domain assumption The gaugeless Hamiltonian formulation correctly captures the dynamics of SU(2) lattice gauge theory with fundamental fermions.
Explicitly invoked in the abstract as the working framework.
domain assumption Tensor-network truncation errors remain small enough not to alter the qualitative scattering behavior at the chosen bond dimensions.
Implicit in any tensor-network simulation claim; not quantified in abstract.

pith-pipeline@v0.9.0 · 5470 in / 1309 out tokens · 54398 ms · 2026-05-10T18:25:01.518789+00:00 · methodology

discussion (0)

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Relation between the paper passage and the cited Recognition theorem.

We present a first real-time study of hadronic scattering in a (1+1)-dimensional SU(2) lattice gauge theory with fundamental fermions using tensor-network techniques... At strong coupling, the B=0 and B=2 channels exhibit predominantly elastic dynamics closely resembling the U(1) Schwinger model. The mixed B=1 sector displays qualitatively new behavior: meson and baryon wavepackets become entangled...

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 2 Pith papers

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

Tightening energy-based boson truncation bound using Monte Carlo-assisted methods
hep-lat 2026-04 unverdicted novelty 7.0

Monte Carlo-assisted tightening of the energy-based boson truncation bound substantially reduces volume dependence in (1+1)D scalar field theory and (2+1)D U(1) gauge theory.
Tightening energy-based boson truncation bound using Monte Carlo-assisted methods
hep-lat 2026-04 unverdicted novelty 7.0

A Monte Carlo-assisted analytic method tightens energy-based bounds on boson truncation errors, substantially reducing the volume dependence of the required cutoff in scalar and gauge theories.

Reference graph

Works this paper leans on

11 extracted references · 7 canonical work pages · cited by 1 Pith paper · 1 internal anchor

[1]

Maximum Entropy Analysis of the Spectral Functions in Lattice QCD

M. Asakawa, T. Hatsuda, Y . Nakahara, Maximum entropy analysis of the spectral functions in lattice QCD, Prog. Part. Nucl. Phys. 46 (2001) 459–508.arXiv:hep-lat/0011040; M. Bruno, M. T. Hansen, Variations on the Maiani-Testa approach and the inverse problem, JHEP 06 (2021) 043.arXiv:2012.11488

work page Pith review arXiv 2001
[2]

Zohar, Phil

E. Zohar, Quantum simulation of lattice gauge theories in more than one space dimension—requirements, chal- lenges and methods, Phil. Trans. A. Math. Phys. Eng. Sci. 380 (2216) (2021) 20210069.arXiv:2106.04609; M. C. Bañuls, et al., Simulating Lattice Gauge Theories within Quantum Technologies, Eur. Phys. J. D 74 (8) (2020) 165.arXiv:1911.00003; L. Funcke...

work page arXiv 2021
[3]

M. C. Bañuls, K. Cichy, J. I. Cirac, K. Jansen, S. Kühn, Tensor Networks and their use for Lattice Gauge Theories, PoS LATTICE2018 (2018) 022.arXiv:1810.12838

work page arXiv 2018
[4]

Papaefstathiou, J

I. Papaefstathiou, J. Knolle, M. C. Bañuls, Real-time scattering in the lattice Schwinger model, Phys. Rev. D 111 (1) (2025) 014504.arXiv:2402.18429; Y . Chai, A. Crippa, K. Jansen, S. Kühn, V . R. Pascuzzi, F. Tacchino, I. Tavernelli, Fermionic wave packet scattering: a quantum computing approach, Quantum 9 (2025) 1638.arXiv:2312.02272; J. Barata, E. Ric...

work page arXiv 2025
[5]

Hadronic scattering in (1+1)D SU(2) lattice gauge theory from tensor networks

J. Barata, J. Hormaza, Z.-B. Kang, W. Qian, Hadronic scattering in (1+1)D SU(2) lattice gauge theory from tensor networks (10 2025).arXiv:2511.00154

work page internal anchor Pith review arXiv 2025
[6]

S. R. Coleman, More About the Massive Schwinger Model, Annals Phys. 101 (1976) 239

1976
[7]

J. B. Kogut, L. Susskind, Hamiltonian Formulation of Wilson’s Lattice Gauge Theories, Phys. Rev. D 11 (1975) 395–408; L. Susskind, Lattice Fermions, Phys. Rev. D 16 (1977) 3031–3039

1975
[8]

Fishman, S

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

2022
[9]

Schollwöck, The density-matrix renormalization group in the age of matrix product states, Annals of physics 326 (1) (2011) 96–192

U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Annals of physics 326 (1) (2011) 96–192

2011
[10]

Haegeman, J

J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pizorn, H. Verschelde, F. Verstraete, Time-Dependent Variational Principle for Quantum Lattices, Phys. Rev. Lett. 107 (2011) 070601.arXiv:1103.0936

work page arXiv 2011
[11]

T. K. Kvorning, L. Herviou, J. H. Bardarson, Time-evolution of local information: thermalization dynamics of local observables, SciPost Phys. 13 (4) (2022) 080.arXiv:2105.11206; C. Artiaco, T. Klein Kvorn- ing, D. Aceituno Chávez, L. Herviou, J. H. Bardarson, Universal Characterization of Quantum Many-Body States through Local Information, Phys. Rev. Lett...

work page arXiv 2022