Quantum Singwi-Tosi-Land-Sjoelander approach for interacting inhomogeneous systems under electromagnetic fields: Comparison with exact results

TL;DR

This paper extends the semi-classical STLS approach to quantum inhomogeneous systems under electromagnetic fields, deriving response functions and validating them against exact solutions for a two-electron system.

Contribution

It introduces a quantum STLS method for inhomogeneous systems and demonstrates its effectiveness by comparing with exact results for a solvable two-electron model.

Findings

STLS response function matches exact results for low-energy excitations

The approach accurately estimates interaction energy contributions

Validates the quantum STLS method for specific inhomogeneous systems

Abstract

For inhomogeneous interacting electronic systems under a time-dependent electromagnetic perturbation, we derive the linear equation for response functions in a quantum mechanical manner. It is a natural extension of the original semi-classical Singwi-Tosi-Land-Sjoelander (STLS) approach for an electron gas. The factorization ansatz for the two-particle distribution is an indispensable ingredient in the STLS approaches for determination of the response function and the pair correlation function. In this study, we choose an analytically solvable interacting two-electron system as the target for which we examine the validity of the approximation. It is demonstrated that the STLS response function reproduces well the exact one for low-energy excitations. The interaction energy contributed from the STLS response function is also discussed.