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

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.Comment: 6 pages, revised, Fig. 2 adde

Approximate formula for the macroscopic polarization including quantum fluctuations

The many-body Berry phase formula for the macroscopic polarization is approximated by a sum of natural orbital geometric phases with fractional occupation numbers accounting for the dominant correlation effects. This reduced formula accurately reproduces the exact polarization in the Rice-Mele-Hubbard model across the band insulator-Mott insulator transition. A similar formula based on a one-body reduced Berry curvature accurately predicts the interaction-induced quenching of Thouless topological charge pumping

Model Hamiltonian for strongly-correlated systems: Systematic, self-consistent, and unique construction

An interacting lattice model describing the subspace spanned by a set of strongly-correlated bands is rigorously coupled to density functional theory to enable ab initio calculations of geometric and topological material properties. The strongly-correlated subspace is identified from the occupation number band structure as opposed to a mean-field energy band structure. The self-consistent solution of the many-body model Hamiltonian and a generalized Kohn-Sham equation exactly incorporates momentum-dependent and crystal-symmetric correlations into electronic structure calculations in a way that does not rely on a separation of energy scales. Calculations for a multiorbital Hubbard model demonstrate that the theory accurately reproduces the many-body polarization.Comment: 19 pages, 11 figure

Adiabatic perturbation theory for two-component systems with one heavy component

A systematic adiabatic perturbation theory with respect to the kinetic energy of the heavy component of a two-component quantum system is introduced. The effective Schr\"odinger equation for the heavy system is derived to second order in the inverse mass. It contains a new form of kinetic energy operator with a Hermitian mass tensor and a complex-valued vector potential. All of the potentials in the effective equation can be computed without having to evaluate sums over the eigenstates of the light system. The most salient potential application of the theory is to systems of electrons and nuclei. The accuracy of the theory is verified numerically in a model of a diatomic molecule and analytically in a linear vibronic model