Time-dependent exchange-correlation functional for a Hubbard dimer: Quantifying nonadiabatic effects

JOHANNA I FUKS; MEHDI FARZANEHPOUR; ILYA V. TOKATLY; HEIKO APPEL; STEFAN KURTH; ANGEL RUBIO

PHYSICAL REVIEW A - ATOMIC, MOLECULAR AND OPTICAL PHYSICS

AMER PHYSICAL SOC

Lugar: New York; Año: 2013 vol. 88

1050-2947

We address and quantify the role of nonadiabaticity (?memory effects?) in the exchange-correlation (xc)functional of time-dependent density functional theory (TDDFT) for describing nonlinear dynamics of many-bodysystems. Time-dependent resonant processes are particularly challenging for available TDDFT approximations,due to their strong nonlinear and nonadiabatic character. None of the known approximate density functionalsare able to cope with this class of problems in a satisfactory manner. In this work we look at the prototypicalexample of the resonant processes by considering Rabi oscillations within the exactly soluble two-site Hubbardmodel. We construct the exact adiabatic xc functional and show that (i) it does not reproduce correctly resonantRabi dynamics, and (ii) there is a sizable nonadiabatic contribution to the exact xc potential, which turns out tobe small only at the beginning and at the end of the Rabi cycle when the ground-state population is dominant. Wethen propose a ?two-level? approximation for the time-dependent xc potential which can capture Rabi dynamicsin the two-site problem. It works well both for resonant and for detuned Rabi oscillations and becomes essentiallyexact in the linear response regime.