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

TL;DR

Problem: understanding real-time, non-perturbative scattering in non-Abelian gauge theories. Approach: real-time tensor-network simulations of a (1+1)D SU(2) lattice gauge theory with gaugeless Hamiltonian across B=0,1,2 sectors. Findings: elastic dynamics dominate for B=0 and B=2; B=1 exhibits meson–baryon entanglement and momentum-dependent delocalization; observables including entanglement entropy and the information lattice quantify correlation buildup. Significance: provides a first-principles benchmark for non-Abelian real-time scattering and lays groundwork for quantum-simulation studies of baryon-number dynamics and inelastic processes, with routes to accessing inelastic channels via flux truncation or expanded Hilbert space.

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.

Figures (10)

• Figure 1: Schematic for the SU(2) scattering process: (a) qubit encoding for the SU(2) states; (b) state preparation for the hadron wavepackets at strong coupling; (c) illustration of the spacetime structure of the scattering process.
• Figure 2: Meson to baryon mass ratio at evaluated with $N=60$ qubits compared with the analytical strong coupling estimation. Here $x = 1/(ga)^2$ and the strong coupling limit corresponds to $1/x\gg 1$.
• Figure 3: Preparation of the wavepackets with different quantum number $B=0,-1, 1$. Momentum dependence of a single wavepacket is included.
• Figure 4: Condensate, baryon number and chromoelectric energy of two meson scattering using $N=60$ qubits. Left column shows results when both mesons are propagate at their maximal momenta; right column shows results for the case of initial states with different momenta.
• Figure 5: Entropy and particle projection of two mesons scattering using $N=60$ qubits. Left column shows results when both mesons are at maximal momenta; right column shows results for the case of initial states with different momenta.