Real-Time String Dynamics in a $2+1$D Non-Abelian Lattice Gauge Theory: String Breaking, Glueball Formation, Baryon Blockade, and Tension Reduction

TL;DR

This work demonstrates real-time, non-Abelian string dynamics in a 2+1D SU$(2)$ lattice gauge theory with dynamical matter using tree tensor networks, accessing larger timescales and system sizes than current quantum simulators. The authors develop a dressed-site formulation with background charges, enforcing gauge invariance and enabling controlled truncations (e.g., hardcore-gluon with $j_{ ext{max}}=1/2$) while preserving non-Abelian features. They uncover distinctive phenomena: resonance-driven string breaking with baryon-antibaryon production, a baryon blockade delaying breaking at finite density, glueball formation and self-crossing strings away from resonance, and representation-dependent tension-reduction resonances at higher $j$. These findings illuminate confinement dynamics in higher dimensions and offer concrete targets for near-term quantum simulations and advanced tensor-network methods in non-Abelian LGTs.

Abstract

Understanding flux string dynamics can provide insight into quark confinement and hadronization. First-principles quantum and numerical simulations have mostly focused on toy-model Abelian lattice gauge theories (LGTs). With the advent of state-of-the-art quantum simulation experiments, it is important to bridge this gap and study string dynamics in non-Abelian LGTs beyond one spatial dimension. Using tensor network methods, we simulate the real-time string dynamics of a $2\!+\!1$D SU$(2)$ Yang--Mills LGT with dynamical matter. In the strong-coupling regime and at resonance, string breaking occurs through sharp Casimir reduction along with meson and baryon-antibaryon formation, a distinctively non-Abelian feature. At finite baryon density, we discover a \textit{baryon blockade} mechanism that delays string breaking. Away from resonance, the magnetic term drives purely non-Abelian fluctuations: glueball loops and self-crossed strings that resolve two SU$(2)$ intertwiners with distinct dynamics. For higher-energy strings, we uncover representation-dependent tension-reduction resonances. Our findings serve as a guide for upcoming quantum simulators of non-Abelian LGTs.

Figures (8)

• Figure 1: Real-time string dynamics in a $2\!+\!1$D SU$(2)$ LGT. On a square lattice with staggered SU$(2)$ dynamical matter fields on sites and SU$(2)$ gauge fields on links, a generic string is created by connecting two static background SU$(2)$ charges within a (gray) patch. In a strong-coupling regime, the string undergoes two scenarios: (a) string breaking (and, more generally, tension reduction), where string links downgrade their Casimir $j\to j-\space{\frac{1}{2}}\space$, allowing for meson and baryon creation; (b) string oscillations, where magnetic effects allow for glueballs and self-crossing strings. This scheme is for illustration purposes only; throughout this work, we consider a $4\!\times\!4$ string patch on an $8\!\times\!8$ lattice.
• Figure 2: String breaking vs. oscillations. String dynamics starting from a minimal L-string. String breaking at the resonance $m_{}\!=\!\tfrac{3}{8}\,g_{E}$ manifest in the (a) decay of string-manifold overlaps over time, (b) decay of the Casimir and increase in the populations of mesons and baryons, defined in \ref{['eq_local_observables']}, and (c) a rapid continual growth in the entanglement entropy. Out of resonance, persistent string oscillations appear where (d) the probability of being in a string is always close to unity, (e) matter creation is suppressed, and (f) entanglement entropy saturates at later times.
• Figure 3: Glueball and self-crossing string formation. String oscillations starting from a maximal S-string. Among all the degenerate string configurations $\mathcal{P}_{k}$ (whose sum stays close to unity) available out of resonance, we highlight in (a) the superpositions of type-ss and type-tt self-crossing strings and loop configurations (glueballs) of single and double loops, respectively. The lower panel shows how four $j=\space{\frac{1}{2}}\space$ (cyan) gauge links can fuse into a singlet using the SU$(2)$ intertwiner scheme: the ss-type (b), where each link pair intermediately fuses to $j=0$ (black), and the tt-type where each link pair intermediately fuses to $j=1$ (dark blue).
• Figure 4: Baryon blockade. Effect of the baryon number sector $N_{\rm{bar}}$ on the string-breaking mechanism in terms of the first observed minimum ($t_{\rm{break}}$) in the time evolution of the Casimir operator. The inset panel shows the scaling of $t_{\rm{break}}$ as a function of the baryon number sector $N_{\rm{bar}}$.
• Figure 5: String tension reduction mechanism. At the resonance $R_{j=1}: m_{}\!=\!\tfrac{5}{8}g_{E}$, the $j\!=\!1$ initial L-string reduces its tension from $C=2\tfrac{\mathcal{L}_{\rm{active}}}{\mathcal{L}_{\rm{patch}}}$ (upper dashed line) towards $C\gtrsim\tfrac{3}{4}\tfrac{\mathcal{L}_{\rm{active}}}{\mathcal{L}_{\rm{patch}}}$ (lower dashed line) through meson and baryon creation while not being broken.