Repulsively diverging gradient of the density functional in the Reduced Density Matrix Functional Theory

• URL: http://arxiv.org/abs/2103.17069v6
• Date: Tue, 19 Oct 2021 10:44:13 GMT
• Title: Repulsively diverging gradient of the density functional in the Reduced Density Matrix Functional Theory
• Authors: Tomasz Maci\k{a}\.zek
• Abstract summary: We show that the existence of the Bose-Einstein condensation force is completely universal for any type of pair-interaction. We also show the existence of an analogous repulsive gradient in the fermionic RDMFT for the $N$-fermion singlet sector.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Reduced Density Matrix Functional Theory (RDMFT) is a remarkable tool for studying properties of ground states of strongly interacting quantum many body systems. As it gives access to the one-particle reduced density matrix of the ground state, it provides a perfectly tailored approach to studying the Bose-Einstein condensation or systems of strongly correlated electrons. In particular, for homogeneous Bose-Einstein condensates as well as for the Bose-Hubbard dimer it has been recently shown that the relevant density functional exhibits a repulsive gradient (called the Bose-Einstein condensation force) which diverges when the fraction of non-condensed bosons tends to zero. In this paper, we show that the existence of the Bose-Einstein condensation force is completely universal for any type of pair-interaction and also in the non-homogeneous gases. To this end, we construct a universal family of variational trial states which allows us to suitably approximate the relevant density functional in a finite region around the set of the completely condensed states. We also show the existence of an analogous repulsive gradient in the fermionic RDMFT for the $N$-fermion singlet sector in the vicinity of the set of the Hartree-Fock states. Finally, we show that our approximate functional may perform well in electron transfer calculations involving low numbers of electrons. This is demonstrated numerically in the Fermi-Hubbard model in the strongly correlated limit where some other approximate functionals are known to fail.

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