Reduced density-matrix functionals from many-particle theory

Abstract

Abstract. In materials with strong electron correlation the proper treatment of local atomic physics described by orbital occupations is crucial. Reduced density-matrix functional theory is a natural extension of density functional theory for systems that are dominated by orbital physics. We review the current state of reduced density-matrix functional theory (RDMFT). For atomic structure relaxations or abinitio molecular dynamics the combination of density functional theory (DFT) and dynamical mean-field theory (DMFT) possesses a number of disadvantages, like the cumbersome evaluation of forces. We therefore describe a method, DFT+RDMFT, that combines many-particle effects based on reduced density-matrix functional theory with a density functional-like framework. A recent development is the construction of density-matrix functionals directly from many-particle theory such as methods from quantum chemistry or many-particle Green's functions. We present the underlying exact theorems and describe current progress towards quantitative functionals.

On the time evolution of fermionic occupation numbers

“…(18) and Eq. (10). Therefore, in the basis of phase-shifted natural orbitals, the Slater-geometrical phase does not contribute to the time evolution of the natural occupation numbers.…”

“…By optimizing the functional A Φ BD with respect to the phases, one obtains an explicit equation for the evolution of the square amplitudes. The time derivative of the Borland-Dennis wave function (10) gives Φ BD |i∂ t |Φ BD = ∑ α f α (ξ α + ϕ α |i∂ t |ϕ α ). We have used the fact that ∑ αḟα = 0 and ϕ β |∂ t |ϕ α = 0 for β = α, because two different Slater determinants in Eq.…”

“…Thus, ground states can be viewed as functionals of such reduced densities (say, Ψ gs [γ]) 6 . Since γ accounts for fractional natural occupation numbers (i.e., its eigenvalues), employing this matrix as the main object leads to a theory able to capture quite well strong (static) electron correlations [7][8][9][10] . For instance, unlike density functional theory, such a densitymatrix functional theory correctly predicts the insulating behavior of Mott-type insulators 11,12 .…”

Hohenberg–Kohn Theorems for Interactions, Spin and Temperature

“…Hence, N i=1 v(x i )+B(x i )·σ i is continuous on (L n ) N . We take the limit n → +∞ and use that the map giving the eigenvalues of a matrix is continuous, to infer that For Gilbert [22], Matrix DFT is extensively used in quantum chemistry [5,6,13,31,35,40,47,64,65,69,72]. This method is similar to standard DFT but the central internal quantity is now the one-particle reduced density matrix (1RDM) which is defined by…”

Dynamical mean-field approach with predictive power for strongly correlated materials

“…The properties of Fe and FeSe determined within this approach are discussed. Schade et al [11] review the current state of reduced density-matrix functional theory, which is a natural extension of DFT for systems dominated by orbital physics. They describe a method which combines many-particle effects based on reduced densitymatrix functional theory with a density functional-like framework, and present the construction of density-matrix functionals directly from many-particle theory such as methods from quantum chemistry or many-particle Greens functions.…”