The perils of minimal coupling to electromagnetic field in quantum many-body systems

TL;DR

This paper highlights the risks of simplifying electromagnetic coupling in quantum many-body models, emphasizing the importance of self-consistent internal EMF treatment especially at low frequencies to avoid inaccurate results.

Contribution

It demonstrates that replacing the internal EMF with an external one in models can lead to significant errors, particularly in non-equilibrium dynamics at low frequencies.

Findings

Replacing internal EMF with external EMF can be dangerous at low frequencies.

Self-consistent treatment of EMF is crucial for accurate modeling.

Simplifications may lead to incorrect predictions in pump-probe experiments.

Abstract

Consistency with the Maxwell equations determines how matter must be coupled to the electro-magnetic field (EMF) within the minimal coupling scheme. Specifically, if the Hamiltonian includes just a short-range repulsion among the conduction electrons, as is commonly the case for models of correlated metals, those electrons must be coupled to the full internal EMF, whose longitudinal and transverse components are self-consistently related to the electron charge and current densities through Gauss's and circuital laws, respectively. Since such self-consistency relation is hard to implement when modelling the non-equilibrium dynamics caused by the EMF, as in pump-probe experiments, it is common to replace in model calculations the internal EMF by the external one. Here we show that such replacement may be extremely dangerous, especially when the frequency of the external EMF is below the intra-band plasma edge.