Excitonic effects in time-dependent density-functional theory: An analytically solvable model

TL;DR

This paper explores how excitonic effects can be accurately described within time-dependent density-functional theory (TDDFT) by establishing an exact link to the Bethe-Salpeter equation, verified through an analytically solvable model.

Contribution

It derives an exact diagrammatic representation of the exchange-correlation kernel in TDDFT and demonstrates its effectiveness in describing excitonic effects with a simple model.

Findings

First-order approximation of f_xc^Ex suffices under certain conditions

TDDFT can match BSE in describing bound excitons

Analytical model confirms the cancellation effects in the kernel

Abstract

We investigate the description of excitonic effects within time-dependent density-functional theory (TDDFT). The exchange-correlation kernel f_xc introduced in TDDFT allows a clear separation of quasiparticle and excitonic effects. Using a diagrammatic representation for f_xc, we express its excitonic part f_xc^Ex in terms of the effective vertex function Lambda. The latter fulfills an integral equation which thereby establishes the exact correspondence between TDDFT and the standard many-body approach based on Bethe-Salpeter equation (BSE).The diagrammatic structure of the kernel in the equation for Lambda suggests the possibility of strong cancellation effects. Should the cancellation take place, already the first-order approximation to f_xc^Ex is sufficient. A potential advantage of TDDFT over the many-body BSE method is thus dependent on the efficiency of the above-quoted cancellation. We explicitly verify this for an analytically solvable two-dimensional two-band model. The calculations confirm that the low-order f_xc^Ex perfectly describes the bound exciton as well as the excitonic effects in the continuous spectrum in a wide range of the electron--hole coupling strength.