Orbital-free quasidensity functional theory

Abstract

We develop an orbital-free functional framework to compute one-body quasiprobabilities for both fermionic and bosonic systems. Since the key variable is a quasidensity, this theory circumvents the problems of finding the Pauli potential or approximating the kinetic energy that are known to limit the applicability of standard orbital-free density functional theory. We present a set of strategies to (a) compute the one-body Wigner quasiprobability in an orbital-free manner from the knowledge of the universal functional and (b) obtain those functionals from the functionals of the one-body reduced density matrix (1-RDM). We find that the universal functional of optical lattices results from a translation, a contraction, and a rotation of the corresponding functional of the 1-RDM, revealing the strong connection between these two functional theories. Furthermore, we relate the key concepts of Wigner negativity and v representability.