Entanglement scaling and dynamics in the Sauter-Schwinger effect

TL;DR

This work investigates how entanglement entropy encodes nonperturbative vacuum decay in scalar QED under a Sauter pulse. Using Gaussian-state formalism and a cylindrical mode basis, the authors connect momentum-space pair production, characterized by mode squeezing and the IR spectrum, to real-space entanglement across cylindrical subregions. They demonstrate a transition from area-law entanglement in the vacuum to power-law and, in strong-field regimes, volume-law scaling as a function of subsystem size, with an explicit L-shaped region in the pulse-parameter space where near-volume-law behavior emerges. These results reveal how nonlocal partner-mode correlations and near-thermal low-energy spectra drive collective entanglement in real space, providing a diagnostic bridge between nonperturbative QED dynamics and information-theoretic measures. The methodology and findings offer a path to exploring similar phenomena in fermionic QED, curved spacetime analogues, and backreaction-enabled regimes, with potential implications for interpreting entanglement signatures in strong-field experiments and holographic contexts.

Abstract

In quantum field theory, entanglement entropy under spatial bipartitioning serves as a powerful information-theoretic probe of quantum correlations. In this work, we present the first comprehensive numerical study of the dynamical evolution and geometric scaling of entanglement entropy in a nonperturbative, strong-field QED setting -- specifically, in the context of the Sauter-Schwinger effect. While the weak-field regime is dominated by area-law states, we show that the entanglement entropy undergoes a transition from area-law to a volume-law scaling for certain strong-field regimes in the pulse-profile parameter space -- signaling a fundamental shift in the underlying correlation structure induced by nonperturbative pair production. For intermediate regimes, the scaling is a power-law that interpolates between area- and volume-law behavior. Finally, we provide interpretations based on the behavior of the low-energy pair-creation spectrum and discuss how these insights could inform future investigations of related phenomena.

Figures (8)

• Figure 1: Overlap ($\zeta$) of the Sauter-Schwinger spectrum for the IR mode ($\omega_{\mathbf{k}}^+=\mu$) with the limiting forms in \ref{['eq:regimes']} corresponding to Regimes A (red) and B (blue). The contour step size is 0.495, with $\zeta>0.99$ indicating high overlap.
• Figure 2: Pairwise entanglement entropy $S_{\mathbf{k}}$ in the Sauter-Schwinger effect for the IR mode $\omega_{\mathbf{k}}^+=\mu$.
• Figure 3: Left: Conventional lattice regularization in cylindrical coordinates. Right: Dimensionally reduced representation, yielding an effective 1+1-dimensional lattice theory.
• Figure 4: The final state ($t/\tau =10^{20}$) correlation structure for the $l=m=0$ sector in (a) the weak-field regime, and (b) the strong-field regime. The emergence of nonlocal correlation peaks in the latter indicates pair creation due to Sauter-Schwinger effect. Here, $\tilde{\mu}=1$ and $N_\varrho=300$.
• Figure 5: Subsystem scaling of entanglement entropy in (a) the vacuum state for $N_\varrho=100$, and (b) the final state ($t/\tau=10^{20}$) when $\xi=10^2$, $\eta=10$ for various values of $N_\varrho$. Here, we set $\tilde{\mu}=1$ and $N_z=100$.