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

Journal Article · · Physical Review A
 [1];  [2];  [3];  [4]
  1. Freie Univ. Berlin, Berlin (Germany); Max Planck Institute of Microstructure Physics, Halle (Germany)
  2. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  3. Max Planck Institute for the Structure and Dynamics of Matter, Hamburg (Germany)
  4. Max Planck Institute of Microstructure Physics, Halle (Germany)

Here, we derive an intrinsically temperature-dependent approximation to the correlation grand potential for many-electron systems in thermodynamical equilibrium in the context of finite-temperature reduced-density-matrix-functional theory (FT-RDMFT). We demonstrate its accuracy by calculating the magnetic phase diagram of the homogeneous electron gas. We compare it to known limits from highly accurate quantum Monte Carlo calculations as well as to phase diagrams obtained within existing exchange-correlation approximations from density functional theory and zero-temperature RDMFT.

Research Organization:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
Grant/Contract Number:
AC04-94AL85000; 200202; NA0003525
OSTI ID:
1421860
Alternate ID(s):
OSTI ID: 1413812
Report Number(s):
SAND-2017-13495J; PLRAAN; 659501; TRN: US1801577
Journal Information:
Physical Review A, Vol. 96, Issue 6; ISSN 2469-9926
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 7 works
Citation information provided by
Web of Science

References (69)

Combining density-functional theory and density-matrix-functional theory journal November 2010
Momentum distribution of the uniform electron gas: Improved parametrization and exact limits of the cumulant expansion journal December 2002
Ab Initio Description of High-Temperature Superconductivity in Dense Molecular Hydrogen journal June 2008
An improved density matrix functional by physically motivated repulsive corrections journal May 2005
Exchange-correlation potential for inhomogeneous electron systems at finite temperatures journal December 1980
Jupiter Models with Improved ab Initio Hydrogen Equation of State (H-Reos.2) journal April 2012
Quantum Monte Carlo study of the three-dimensional spin-polarized homogeneous electron gas journal August 2013
Density-matrix-power functional: Performance for finite systems and the homogeneous electron gas journal April 2009
Spin polarization of the low-density three-dimensional electron gas journal September 2002
Path-Integral Monte Carlo Simulation of the Warm Dense Homogeneous Electron Gas journal April 2013
Spin-polarized electron liquid at arbitrary temperatures:  Exchange-correlation energies, electron-distribution functions, and the static response functions journal December 2000
Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis journal August 1980
Collective electron ferronmagnetism journal April 1938
Shock Compression of a Fifth Period Element: Liquid Xenon to 840 GPa journal August 2010
Discontinuity of the chemical potential in reduced-density-matrix-functional theory journal March 2007
Benchmark calculations for reduced density-matrix functional theory journal May 2008
Performance of one-body reduced density-matrix functionals for the homogeneous electron gas journal May 2007
Hot-electron-assisted femtochemistry at surfaces: A time-dependent density functional theory approach journal May 2009
Superconductivity in Lithium, Potassium, and Aluminum under Extreme Pressure: A First-Principles Study journal February 2006
Excited-state density functional theory journal November 2012
Structure of Fermion Density Matrices journal July 1963
Minimization procedure in reduced density matrix functional theory by means of an effective noninteracting system journal January 2013
Spin-polarized Hartree-Fock approximation at nonzero temperatures journal June 1995
Noncollinear spin-spiral phase for the uniform electron gas within reduced-density-matrix-functional theory journal January 2010
A Collective Description of Electron Interactions: III. Coulomb Interactions in a Degenerate Electron Gas journal November 1953
Finite-temperature study of itinerant ferromagnetism in Fe, Co, and Ni journal June 1997
Demixing of Hydrogen and Helium at Megabar Pressures journal March 2009
Pair-distribution functions of two-temperature two-mass systems: Comparison of molecular dynamics, classical-map hypernetted chain, quantum Monte Carlo, and Kohn-Sham calculations for dense hydrogen journal February 2008
Accurate Homogeneous Electron Gas Exchange-Correlation Free Energy for Local Spin-Density Calculations journal February 2014
Temperature dependence of the Hartree-Fock approximation journal September 1994
Correlation Energy and Spin Polarization in the 2D Electron Gas journal June 2002
Self-Consistent Equations Including Exchange and Correlation Effects journal November 1965
Density-functional theory of hydrogen plasmas journal October 1982
Density functional formalism at finite temperatures with some applications journal July 1982
Communications: Accurate description of atoms and molecules by natural orbital functional theory journal January 2010
Exchange-correlation energy for the three-dimensional homogeneous electron gas at arbitrary temperature journal August 2013
Inhomogeneous Phase Formation on the Border of Itinerant Ferromagnetism journal November 2009
Computational Complexity and Fundamental Limitations to Fermionic Quantum Monte Carlo Simulations journal May 2005
Short-range correlations and the structure factor and momentum distribution of electrons journal September 1975
Quantum Theory of Many-Particle Systems. I. Physical Interpretations by Means of Density Matrices, Natural Spin-Orbitals, and Convergence Problems in the Method of Configurational Interaction journal March 1955
New Method for Calculating the One-Particle Green's Function with Application to the Electron-Gas Problem journal August 1965
On the infinitude of non–zero eigenvalues of the single–electron density matrix for atoms and molecules journal January 2003
Universal variational functionals of electron densities, first-order density matrices, and natural spin-orbitals and solution of the v-representability problem journal December 1979
The Physics of Inertial Fusion book January 2004
An approximate exchange-correlation hole density as a functional of the natural orbitals journal February 2002
Analysis of density functionals and their density tails in H2 journal January 1998
The phase diagram of water and the magnetic fields of Uranus and Neptune journal January 2011
Inhomogeneous Electron Gas journal November 1964
Quantum Theory of the Electron Liquid book August 2012
Accurate and simple analytic representation of the electron-gas correlation energy journal June 1992
Reduced-density-matrix-functional theory at finite temperature: Theoretical foundations journal November 2015
A density matrix functional with occupation number driven treatment of dynamical and nondynamical correlation journal October 2008
Ground State of the Electron Gas by a Stochastic Method journal August 1980
Path integrals in the theory of condensed helium journal April 1995
Discontinuities of the Chemical Potential in Reduced Density Matrix Functional Theory journal April 2010
Geometry of density matrices. II. Reduced density matrices and N representability journal April 1978
Spin Density Waves in an Electron Gas journal November 1962
Metallization in hydrogen-helium mixtures journal December 2011
New indication for a dichotomy in the interior structure of Uranus and Neptune from the application of modified shape and rotation data journal March 2013
Density Functional Theory of Normal and Superconducting Electron Liquids: Explicit Functionals via the Gradient Expansion journal January 1996
Shock Compression of Quartz to 1.6 TPa: Redefining a Pressure Standard journal November 2009
Thermal Properties of the Inhomogeneous Electron Gas journal March 1965
Local Approximation of the Correlation Energy Functional in the Density Matrix Functional Theory journal January 2002
Correlation energy functional within the G W -RPA: Exact forms, approximate forms, and challenges journal May 2010
Local Density Approximation for Superconductors journal September 1999
Perspective on density functional theory journal April 2012
Empirical functionals for reduced-density-matrix-functional theory journal March 2008
Reduced density matrix functional for many-electron systems journal November 2008
Explicit approximate relation between reduced two- and one-particle density matrices journal November 1984