Real-time simulation of the Schwinger effect with Matrix Product States

TL;DR

This paper demonstrates real-time simulation of the Schwinger effect using Matrix Product States, revealing oscillatory and thermalization behaviors depending on quench size, and comparing quantum and semi-classical approaches.

Contribution

It introduces a novel application of MPS for simulating real-time dynamics of the Schwinger model, including thermalization insights and comparison with semi-classical methods.

Findings

Oscillatory behavior explained by single-particle excitations for small quenches.

Damped oscillations and possible thermalization for large quenches.

Agreement between MPS simulations and semi-classical approach in large quench limit.

Abstract

Matrix Product States (MPS) are used for the simulation of the real-time dynamics induced by an electric quench on the vacuum state of the massive Schwinger model. For small quenches it is found that the obtained oscillatory behavior of local observables can be explained from the single-particle excitations of the quenched Hamiltonian. For large quenches damped oscillations are found and comparison of the late time behavior with the appropriate Gibbs states seems to give some evidence for the onset of thermalization. Finally, the MPS real-time simulations are explicitly compared with the semi-classical approach and, as expected, agreement is found in the limit of large quenches.