Time-dependent occupation numbers in reduced-density-matrix functional theory: Application to an interacting Landau-Zener model

TL;DR

This paper demonstrates that using ground-state functionals for two-body terms in reduced-density-matrix theory keeps occupation numbers constant, revealing a fundamental limitation and deriving exact phase dynamics in an interacting Landau-Zener model.

Contribution

It identifies a key deficiency in current approximations and derives an exact differential equation for phase behavior in an interacting Landau-Zener system.

Findings

Occupation numbers remain constant with ground-state functional approximations.

Derived an exact differential equation for phase evolution.

Observed resonance phenomena and correlation-induced oscillations.

Abstract

We prove that if the two-body terms in the equation of motion for the one-body reduced density matrix are approximated by ground-state functionals, the eigenvalues of the one-body reduced density matrix (occupation numbers) remain constant in time. This deficiency is related to the inability of such an approximation to account for relative phases in the two-body reduced density matrix. We derive an exact differential equation giving the functional dependence of these phases in an interacting Landau-Zener model and study their behavior in short- and long-time regimes. The phases undergo resonances whenever the occupation numbers approach the boundaries of the interval [0,1]. In the long-time regime, the occupation numbers display correlation-induced oscillations and the memory dependence of the functionals assumes a simple form.