Kohn–Sham equations with functionals from the strictly-correlated regime: investigation with a spectral renormalization method

Abstract

We re-adapt a spectral renormalization method, introduced in nonlinear optics, to solve the Kohn-Sham (KS) equations of density functional theory, with a focus on functionals based on the strictly-correlated electrons (SCE) regime, which are particularly challenging to converge. Important aspects of the method are: (i) the eigenvalues and the density are computed simultaneously; (ii) it converges using randomized initial guesses; (iii) easy to implement. Using this method we could converge for the first time the Kohn-Sham equations with functionals that include the next leading term in the strong-interaction limit of density functional theory, the so called zero-point energy (ZPE) functional as well as with an interaction-strength-interpolation functional that includes both the exact SCE and ZPE terms. This work is the first building block for future studies on quantum systems confined in low dimensions with different statistics and long-range repulsions, such as localization properties of fermions and bosons with strong long-range repulsive interactions in the presence of a random external potential.

Large coupling-strength expansion of the Møller–Plesset adiabatic connection: From paradigmatic cases to variational expressions for the leading terms

“…More recently, the SR method has been applied to converge the self-consistent Kohn-Sham equations with the functionals from the λ → ∞ limit of the density-fixed DFT adiabatic connection. 48 The SR variant we have used here starts from an initial u (0) to compute, via Eq. (20), a first estimate of the eigenvalue ϵ (0)…”

Large coupling-strength expansion of the Møller-Plesset adiabatic connection: From paradigmatic cases to variational expressions for the leading terms

“…More recently, the SR method has been applied to converge the self-consistent Kohn-Sham equations with the functionals from the λ → ∞ limit of the density-fixed DFT adiabatic connection. 46 The SR variant we have used here starts from an initial u (0) to compute, via Eq. ( 20), a first estimate of the eigenvalue…”

Time-Dependent Duhamel Renormalization method with Multiple Conservation and Dissipation Laws

“…In 2005 Ablowitz and Musslimani proposed the spectral renormalization method as a tool to numerically approximate solutions to nonlinear boundary value problems. Since then, it has been successfully used in many physical settings that include photonics [42], Bose-Einstein condensation [7], Kohn-Sham density functional theory [17], and water waves [5]. In 2016, Cole and Musslimani proposed the time dependent spectral renormalization method to simulate evolution equations with periodic boundary conditions.…”