Characterization of the potential entanglement phase transition

Characterize the potential phase transition in the asymptotic logarithmic negativity of localized vacuum correlations under a Sauter-type electric pulse, including its full parameter space and dependence on parameters beyond the dominant control parameter qE_0\Gamma^2.

Background

For a charged scalar field in 1+1-dimensional Minkowski spacetime, the paper studies correlations between localized modes in two adjacent spatial regions subjected to a Sauter-type electric pulse. In the non-perturbative regime, the logarithmic negativity decreases as the pulse strength increases and vanishes at a finite time for sufficiently intense pulses. The asymptotic-future behavior appears threshold-like near qE_0\Gamma^2 \approx 1/2, suggesting a possible phase transition with qE_0\Gamma^2 as a control parameter and the logarithmic negativity as an order parameter.

The authors note that the onset of the transition occurs somewhat below the apparent critical value and may depend on additional parameters, while the small number of modes used in the numerical analysis may produce finite-size effects. A systematic characterization of this potential phase transition and its complete parameter dependence remains unresolved.