String Breaking Dynamics and Glueball Formation in a $2+1$D Lattice Gauge Theory

TL;DR

This work analyzes real-time string dynamics in a 2+1D Z2 lattice gauge theory with dynamical matter using tensor-network simulations and perturbative effective models. It identifies resonance conditions where string breaking occurs via meson production and characterizes off-resonant, confined oscillations through an effective large-$h_x$ framework, including a free-fermion mapping for minimal strings. The authors show that long strings can dynamically nucleate loops that resemble glueballs, offering a QCD-like mechanism in a gauged lattice model. The results provide actionable predictions for quantum simulators and advance understanding of confinement and nonperturbative flux dynamics in higher-dimensional LGTs.

Abstract

With the advent of advanced quantum processors capable of probing lattice gauge theories (LGTs) in higher spatial dimensions, it is crucial to understand string dynamics in such models to guide upcoming experiments and to make connections to high-energy physics (HEP). Using tensor network methods, we study the far-from-equilibrium quench dynamics of electric flux strings between two static charges in the $2+1$D $\mathbb{Z}_2$ LGT with dynamical matter. We calculate the probabilities of finding the time-evolved wave function in string configurations of the same length as the initial string. At resonances determined by the the electric field strength and the mass, we identify various string breaking processes accompanied with matter creation. Away from resonance strings exhibit intriguing confined dynamics which, for strong electric fields, we fully characterize through effective perturbative models. Starting in maximal-length strings, we find that the wave function enters a dynamical regime where it splits into shorter strings and disconnected loops, with the latter bearing qualitative resemblance to glueballs in quantum chromodynamics (QCD). Our findings can be probed on state-of-the-art superconducting-qubit and trapped-ion quantum processors.

Figures (12)

• Figure 1: Dynamical quantum phase diagram of the model \ref{['eq:2DFS']} in the confined/Higgs regimes. Deep in the confined phase one can either observe rich unbroken string dynamics, including quantum revivals and loop nucleation, or string breaking in correspondence of certain mesonic resonances. As the Higgs phase is approached, strings dissipate, and mesons whose mobility is initially restricted spread across the lattice.
• Figure 2: Minimal string probability (top) and total particle number (bottom) as a function of time for the initial state corresponding to an L-shaped string. We take $h_x=4$, $h_z=1$ and $J_p=1$, which places the system in the confined regime. For the first two resonances $J_s^{\text{1}}=2$ and $J_s^{\text{2}}=4$, the string probability drops to very small values at timescales $t^*_1\approx 0.8$ and $t_2^*\approx 5$ respectively. String breaking coincides with the creation of one and two mesons (pairs of $\mathbb{Z}_2$ charges) respectively. In the off-resonance case, matter fluctuations are still present, but the minimal string probability maintains a finite value at large timescales. The black curves show perturbative results valid in the regime where $h_x \rightarrow \infty$ while maintaining the resonance conditions $h_x=2J_s$. To match the numerical results, we choose $J_p=h_z=1$ in the effective model.
• Figure 3: Comparison between perturbative analytical results for the fidelity $\mathcal{F}(t)$ of different initial states, obtained using the free-fermion picture, and numerical TDVP results. We see how deep in the confined regime the perturbative results becomes exact. As the electric coupling $h_x$ is lowered, deviations are increasingly manifest. The parameters of the quench Hamiltonian are $J_p=1$, $J_s=15$, and $h_z=1$.
• Figure 4: (a) Fidelity of the "snake" initial state for different values of the electric field $h_x$. Similarly to the minimal length strings case, we see excellent agreement with the perturbative results at large $h_x$. The parameters for the quench in are $J_p=1$ and $J_s=15$. (b) Perturbative ($h_x\rightarrow \infty$) results for the probability for an initial "snake" string state to nucleate one or more electric loops, resolved by size and number of the loops. (c) Examples of configurations containing simple or extended electric loops.
• Figure S1: Schematics of the geometry used in this study. The red solid line, yellow dots, and blue dashed line represent the initial L-shaped string, the static charges, and the cut used to compute the entanglement entropy respectively.