Density-Functional Theory for Strongly Correlated Bosonic and Fermionic Ultracold Dipolar and Ionic Gases

Abstract

We introduce a density functional formalism to study the ground-state properties of stronglycorrelated dipolar and ionic ultracold bosonic and fermionic gases, based on the self-consistent combination of the weak and the strong coupling limits. Contrary to conventional density functional approaches, our formalism does not require a previous calculation of the interacting homogeneous gas, and it is thus very suitable to treat systems with tunable long-range interactions. Due to its asymptotic exactness in the regime of strong correlation, the formalism works for systems in which standard mean-field theories fail.Introduction -In contrast with its widespread use and success in areas as diverse as quantum chemistry [1], materials science [2] or semiconductor nanostructures [3], Density Functional Theory (DFT) has received relatively little attention in the very active field of ultracold atomic gases. It is well known that the Hohenberg-Kohn theorems, originally formulated in terms of the electron gas [4,5], hold for both fermionic and bosonic systems, as well as for interactions different than the Coulomb one. However, the lack of adequate density functionals has hindered the role of DFT in the study of ultracold atomic gases in favour of other well-established approaches, such as the widely used Gross-Pitaevskii (GP) method in the case of Bose gases. The latter is a mean-field approach and does not allow treating the effect of correlations, which play a crucial role in many different phenomena occurring in ultracold quantum gases [6]. One then often turns to configuration-interaction (CI), quantum Monte Carlo (QMC) or Green's-function methods (for recent reviews, see, e.g., Refs. 6-8).

Exchange–Correlation Functionals via Local Interpolation along the Adiabatic Connection

“…29,[33][34][35][36][37] This limit reveals a new structure for the XC functional: instead of the traditional ingredients of DFAs (local density, density gradients, KS kinetic energy density, occupied and unoccupied KS orbitals) it is observed that certain integrals of the density appear in this limit, encoding highly non-local information. 33,35,[38][39][40] Tests on model physical and chemical systems (electrons confined in low-dimensional geometries and lowdensity, ultracold dipolar systems, simple stretched bonds and anions) have shown 35,37,39,40,[88][89][90] that taking into account this exact behaviour can pave the way for the solution of the strong correlation problem in DFT. However, the exact information encoded in the infinite coupling limit, described by the SCE functional, does not come for free: the SCE problem is ultra non-local, and, although sparse in principle, its non-linearity makes its exact evaluation for general three-dimensional geometry a complex task.…”

The adiabatic strictly-correlated-electrons functional: kernel and exact properties

“…While a considerable amount of work on the strictlycorrelated-electrons (SCE) formalism [1][2][3] within the framework of ground state Kohn-Sham (KS) density functional theory (DFT) has been carried out, [4][5][6][7][8] the study of its performances in the time domain is just starting. 9,10 The aim of this work is to begin a systematic investigation of the SCE functional in the context of time dependent problems, in order to understand its fundamental aspects and its potential in tackling challenging problems for the standard approximations employed in time-dependent (TD) DFT.…”

Simple Fully Nonlocal Density Functionals for Electronic Repulsion Energy

“…19,20 It can be also applied to other isotropic interactions, such as the error function used in range separation 5 but also effective interactions for ultracold quantum gases. 21 …”

“…Instead of the local density, density derivatives or KS orbitals, in this limit we see that certain integrals of the density play a crucial role, encoding highly nonlocal information, [15][16][17] embodied in the so-called strictly-correlated electrons (SCE) functional. [15][16][17] This functional appears to be well-equipped for solving long-standing DFAs problems: it is self-interaction free, it captures the physics of charge localization due to strong correlation without resorting to symmetry breaking, [19][20][21] and its functional derivative displays (in the low-density asymptotic limit) a discontinuity on the onset of fractional particle number. 22 Despite these appealing features, there are two main obstacles to a) Electronic mail: p.gorigiorgi@vu.nl the routine use of the SCE functional: its availability is restricted to small systems 16,23 and its energies are way too low for most of physical and chemical systems.…”