skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Exchange-correlation approximations for reduced-density-matrix-functional theory at finite temperature: Capturing magnetic phase transitions in the homogeneous electron gas

Authors:
; ; ;
Publication Date:
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1413812
Grant/Contract Number:
200202; NA-0003525
Resource Type:
Journal Article: Publisher's Accepted Manuscript
Journal Name:
Physical Review A
Additional Journal Information:
Journal Volume: 96; Journal Issue: 6; Related Information: CHORUS Timestamp: 2017-12-18 10:09:16; Journal ID: ISSN 2469-9926
Publisher:
American Physical Society
Country of Publication:
United States
Language:
English

Citation Formats

Baldsiefen, Tim, Cangi, Attila, Eich, F. G., and Gross, E. K. U. Exchange-correlation approximations for reduced-density-matrix-functional theory at finite temperature: Capturing magnetic phase transitions in the homogeneous electron gas. United States: N. p., 2017. Web. doi:10.1103/PhysRevA.96.062508.
Baldsiefen, Tim, Cangi, Attila, Eich, F. G., & Gross, E. K. U. Exchange-correlation approximations for reduced-density-matrix-functional theory at finite temperature: Capturing magnetic phase transitions in the homogeneous electron gas. United States. doi:10.1103/PhysRevA.96.062508.
Baldsiefen, Tim, Cangi, Attila, Eich, F. G., and Gross, E. K. U. 2017. "Exchange-correlation approximations for reduced-density-matrix-functional theory at finite temperature: Capturing magnetic phase transitions in the homogeneous electron gas". United States. doi:10.1103/PhysRevA.96.062508.
@article{osti_1413812,
title = {Exchange-correlation approximations for reduced-density-matrix-functional theory at finite temperature: Capturing magnetic phase transitions in the homogeneous electron gas},
author = {Baldsiefen, Tim and Cangi, Attila and Eich, F. G. and Gross, E. K. U.},
abstractNote = {},
doi = {10.1103/PhysRevA.96.062508},
journal = {Physical Review A},
number = 6,
volume = 96,
place = {United States},
year = 2017,
month =
}

Journal Article:
Free Publicly Available Full Text
This content will become publicly available on December 18, 2018
Publisher's Accepted Manuscript

Save / Share:
  • In this work, we explore the performance of approximations to electron correlation in reduced density-matrix functional theory (RDMFT) and of approximations to the observables calculated within this theory. Our analysis focuses on the calculation of total energies, occupation numbers, removal/addition energies, and spectral functions. We use the exactly solvable Hubbard dimer at 1/4 and 1/2 fillings as test systems. This allows us to analyze the underlying physics and to elucidate the origin of the observed trends. For comparison, we also report the results of the GW approximation, where the self-energy functional is approximated, but no further hypothesis is made concerningmore » the approximations of the observables. In particular, we focus on the atomic limit, where the two sites of the dimer are pulled apart and electrons localize on either site with equal probability, unless a small perturbation is present: this is the regime of strong electron correlation. In this limit, using the Hubbard dimer at 1/2 filling with or without a spin-symmetry-broken ground state allows us to explore how degeneracies and spin-symmetry breaking are treated in RDMFT. We find that, within the used approximations, neither in RDMFT nor in GW, the signature of strong correlation is present, when looking at the removal/addition energies and spectral function from the spin-singlet ground state, whereas both give the exact result for the spin-symmetry broken case. Moreover, we show how the spectroscopic properties change from one spin structure to the other.« less
  • We propose a method that employs functionals of the one-electron reduced density matrix (density matrix) to capture long-range effects of electron correlation. The complementary short-range regime is treated with density functionals. In an effort to find approximations for the long-range density-matrix functional, a modified power functional is applied to the homogeneous electron gas with Coulomb interactions replaced by their corresponding long-range counterparts. For the power {beta}=1/2 and the range-separation parameter {omega}=1/r{sub s}, the functional reproduces the correlation and the kinetic correlation energies with a remarkable accuracy for intermediate and large values of r{sub s}. Analysis of the Euler equation correspondingmore » to this functional reveals correct r{sub s} expansion of the correlation energy in the limit of large r{sub s}. The first expansion coefficient is in very good agreement with that obtained from the modified Wigner-Seitz model.« less
  • The increasing interest in the Mueller density-matrix-functional theory has led us to a systematic mathematical investigation of its properties. This functional is similar to the Hartree-Fock (HF) functional, but with a modified exchange term in which the square of the density matrix {gamma}(x,x{sup '}) is replaced by the square of {gamma}{sup 1/2}(x,x{sup '}). After an extensive introductory discussion of density-matrix-functional theory we show, among other things, that this functional is convex (unlike the HF functional) and that energy minimizing {gamma}'s have unique densities {rho}(r), which is a physically desirable property often absent in HF theory. We show that minimizers existmore » if N{<=}Z, and derive various properties of the minimal energy and the corresponding minimizers. We also give a precise statement about the equation for the orbitals of {gamma}, which is more complex than for HF theory. We state some open mathematical questions about the theory together with conjectured solutions.« less
  • Thermal density functional theory calculations often use the Mermin-Kohn-Sham scheme, but employ ground-state approximations to the exchange-correlation (XC) free energy. In the simplest solvable nontrivial model, an asymmetric Hubbard dimer, we calculate the exact many-body energies and the exact Mermin-Kohn-Sham functionals for this system and extract the exact XC free energy. For moderate temperatures and weak correlation, we find this approximation to be excellent. Here we extract various exact free-energy correlation components and the exact adiabatic connection formula.