Two-particle irreducible effective action approach to nonlinear current conserving approximations in driven systems

TL;DR

This paper develops a gauge-invariant effective action framework using the closed-time path 2PI approach to accurately compute nonlinear response functions in driven, interacting electronic systems, ensuring current conservation beyond mean-field approximations.

Contribution

It introduces a gauge-invariant 2PI effective action method that guarantees current conservation in nonlinear response calculations for driven electronic systems.

Findings

The CTP 2PI CGEA is gauge invariant at all truncation levels.

Response functions satisfy the Ward-Takahashi hierarchy, ensuring current conservation.

The approach provides a systematic way to compute response functions via Schwinger-Dyson and Bethe-Salpeter equations.

Abstract

Using closed-time path two-particle irreducible coarse-grained effective action (CTP 2PI CGEA) techniques, we study the response of an open interacting electronic system to time-dependent external electromagnetic fields. We show that the CTP 2PI CGEA is invariant under a simultaneous gauge transformation of the external field and the full Schwinger-Keldysh propagator, and that this property holds even when the loop expansion of the CTP 2PI CGEA is truncated at arbitrary order. The effective action approach provides a systematic way of calculating the propagator and response functions of the system, via the Schwinger-Dyson equation and the Bethe-Salpeter equations, respectively. We show that, due to the invariance of the CTP 2PI CGEA under external gauge transformations, the response functions calculated from it satisfy the Ward-Takahashi hierarchy, thus warranting the conservation of the electronic current beyond the expectation value level. We also clarify the connection between nonlinear response theory and the WT hierarchy, and discuss an example of an ad hoc approximation that violate it. These findings may be useful in the study of current fluctuations in correlated electronic pumping devices.