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arxiv: 2511.00154 · v3 · submitted 2025-10-31 · ✦ hep-lat · hep-ph· nucl-th· quant-ph

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

Jo\~ao Barata , Juan Hormaza , Zhong-Bo Kang , Wenyang Qian This is my paper

Pith reviewed 2026-05-18 02:18 UTC · model grok-4.3

classification ✦ hep-lat hep-phnucl-thquant-ph
keywords SU(2) lattice gauge theoryhadronic scatteringtensor networksreal-time dynamicsbaryon numbermeson-baryon collisionentanglement entropygaugeless formulation
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The pith

In (1+1)D SU(2) lattice gauge theory, meson-baryon collisions entangle wave packets and delocalize 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.

This paper applies tensor-network methods to simulate real-time scattering of hadrons in a (1+1)-dimensional SU(2) lattice gauge theory with fundamental fermions. It examines processes in fixed baryon-number sectors and reports that the mixed meson-baryon channel produces entanglement and asymmetric propagation, while same-particle channels remain largely elastic. The work supplies an initial benchmark for non-Abelian real-time dynamics and points toward future quantum-simulation studies of baryon-number evolution.

Core claim

Working in the gaugeless Hamiltonian formulation of (1+1)-dimensional SU(2) lattice gauge theory with fundamental fermions, tensor-network simulations show that in the B=1 sector meson and baryon wave packets become entangled during collision, with the slower state becoming spatially delocalized and the faster one propagating ballistically, in contrast to the predominantly elastic dynamics observed in the B=0 and B=2 sectors.

What carries the argument

tensor-network techniques in the gaugeless Hamiltonian formulation that exactly integrates out the gauge field without truncating electric flux

If this is right

  • Local observables, entanglement entropy, and the information lattice track the buildup and relaxation of correlations during the interaction.
  • The results supply a first benchmark for non-Abelian real-time scattering from first principles.
  • These dynamics open the path toward quantum-simulation studies of baryon-number dynamics and inelastic processes in gauge theories.

Where Pith is reading between the lines

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

  • The observed delocalization may become more pronounced or lead to particle production when the coupling is weakened or the spatial dimension is increased.
  • Similar entanglement patterns could guide the design of initial states for quantum simulators aiming to study real-time QCD-like processes.
  • The contrast between sectors suggests that global baryon number acts as a control parameter for the degree of inelasticity in gauge-theory scattering.

Load-bearing premise

The strong-coupling regime and exact integration of gauge fields without flux truncation capture the essential features of the scattering dynamics in this model.

What would settle it

A simulation or exact calculation on small lattices that shows no entanglement growth or no differential delocalization between slower and faster states in the B=1 sector under matching initial conditions would contradict the reported behavior.

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 -- where the gauge field is exactly integrated out and no truncation of the electric flux is required -- we investigate scattering processes across sectors of fixed global baryon number $B = 0, 1, 2$. These correspond 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 those of the U(1) Schwinger model. In contrast, the mixed $B = 1$ sector shows qualitatively new behavior: meson and baryon wave packets become entangled during the collision, and depending on their initial kinematics, the slower state becomes spatially delocalized while the faster one propagates ballistically. We characterize these processes through local observables, entanglement entropy, and the information-lattice, which together reveal how correlations build up and relax during the interaction. Our results establish a first benchmark for non-Abelian real-time scattering from first principles and open the path toward quantum-simulation studies of baryon-number dynamics and inelastic processes in gauge theories.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 2 minor

Summary. The paper presents a first real-time tensor-network study of hadronic scattering in (1+1)D SU(2) lattice gauge theory with fundamental fermions. Working in the gaugeless Hamiltonian formulation at strong coupling, it examines collisions in fixed baryon-number sectors B=0 (meson-meson), B=1 (meson-baryon), and B=2 (baryon-baryon). It reports predominantly elastic dynamics resembling the Schwinger model in the B=0 and B=2 sectors, while the B=1 sector exhibits qualitatively new behavior in which meson and baryon wave packets entangle, leading to spatial delocalization of the slower state and ballistic propagation of the faster state, characterized via local observables, entanglement entropy, and the information lattice.

Significance. If the results hold, this work provides a valuable first-principles benchmark for non-Abelian real-time scattering in lattice gauge theories and demonstrates the utility of tensor networks for studying baryon-number-dependent dynamics without electric-flux truncation. The use of the information lattice to track correlation buildup and relaxation, together with the clear contrast across sectors, strengthens the case for extending such methods to inelastic processes and quantum-simulation protocols.

major comments (1)
  1. [Abstract and numerical-results section] Abstract and numerical-results section: the central claim that the B=1 sector displays qualitatively new entangled dynamics with asymmetric delocalization is presented exclusively at a fixed strong-coupling value. No variation of the gauge coupling, no scaling analysis, and no comparison to weaker couplings are reported, leaving open whether the observed behavior is robust or specific to the strong-coupling regime where confinement is enhanced and hopping is suppressed.
minor comments (2)
  1. [Abstract] The term 'information-lattice' is used to characterize correlations but receives no brief definition or pointer to its prior introduction in the text; a short explanatory clause would improve accessibility.
  2. [Figure captions] Figure captions for the time-evolution plots should explicitly state the lattice size, bond dimension, and time-step parameters used to generate the data.

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 constructive feedback. We address the single major comment below in a point-by-point manner.

read point-by-point responses

  1. Referee: Abstract and numerical-results section: the central claim that the B=1 sector displays qualitatively new entangled dynamics with asymmetric delocalization is presented exclusively at a fixed strong-coupling value. No variation of the gauge coupling, no scaling analysis, and no comparison to weaker couplings are reported, leaving open whether the observed behavior is robust or specific to the strong-coupling regime where confinement is enhanced and hopping is suppressed.

    Authors: We thank the referee for this observation. The manuscript is deliberately focused on the strong-coupling regime, as stated in the abstract and numerical-results section, because the gaugeless formulation is particularly advantageous there: the exact integration of the gauge field eliminates any need for electric-flux truncation while the suppressed hopping terms accentuate confinement effects and make the non-Abelian signatures in the B=1 sector most visible. This choice yields a clean first benchmark that contrasts sharply with the elastic behavior in the B=0 and B=2 sectors. We agree that a systematic scan in the gauge coupling and a scaling analysis would be required to establish robustness across regimes. Such an extension, however, entails substantially higher computational cost for tensor-network simulations at weaker couplings and lies outside the scope of the present initial study. We will revise the conclusions to include an explicit statement of this limitation together with an outline of planned future work on coupling dependence. revision: partial

Circularity Check

0 steps flagged

No significant circularity in numerical tensor-network simulation results

full rationale

The paper reports outcomes of direct real-time tensor-network evolution of meson and baryon wave packets in the gaugeless Hamiltonian formulation of (1+1)D SU(2) lattice gauge theory. Claims of predominantly elastic scattering in B=0 and B=2 sectors versus entanglement and asymmetric delocalization in the B=1 sector are computational outputs at fixed strong coupling, not quantities obtained by fitting parameters to data and then relabeling the fit as a prediction, nor by self-citation chains that close on themselves. No load-bearing step reduces the reported dynamics to a definition or prior result by construction; the central results remain independent numerical benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central observations rest on the validity of the gaugeless formulation and the choice of strong coupling; no new particles or forces are postulated.

free parameters (1)
  • strong coupling value
    The regime is selected by hand to access the reported dynamics.
axioms (1)
  • domain assumption Gauge field can be exactly integrated out in the gaugeless Hamiltonian formulation without truncation of electric flux
    Invoked to enable the simulation of the full theory in fixed baryon sectors.

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Forward citations

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