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

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.

arXiv commentv6: the published version. New J. Phys 2021

References in corpus (18)

• Condensation of Pairs of Fermionic Atoms Near a Feshbach Resonance
• Experimental Study of the BEC-BCS Crossover Region in Lithium 6
• Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas
• An Atom Laser with a cw Output Coupler
• Reduced Density Matrix Functional for Many-Electron Systems
• The Pauli principle revisited
• Quantum depletion of a homogeneous Bose-Einstein condensate
• The derivative discontinuity of the exchange-correlation functional
• The Excitation Spectrum for Weakly Interacting Bosons
• Relating the pure and ensemble density matrix functional
• Diverging exchange force and form of the exact density matrix functional
• Density-Matrix functional theory of strongly-correlated lattice fermions
• Landscape of an exact energy functional
• Connecting N-representability to Weyl's problem: The one particle density matrix for N = 3 and R = 6
• Reduced Density Matrix Functional Theory for Bosons
• Machine Learning Universal Bosonic Functionals
• Pure Gaussian states from quantum harmonic oscillator chains with a single local dissipative process
• Functional Theory for Bose-Einstein Condensates