2011/05/31 by A. Putaja, E. Räsänen, E. Rasanen · 7 citations
Chemistry · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Ansatz #Chemistry #Constraint (computer-aided design) #Density functional theory #Density matrix #Electron #Energy (signal processing) #Fermi gas #Homogeneous #Mathematical physics #Mathematics #Matrix (chemical analysis) #Physics #Physics of Superconductivity and Magnetism #Quantum #Quantum and electron transport phenomena #Quantum mechanics #Scaling #Statistical physics #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.84.035104
published in Physical Review B 84(3) (American Physical Society)
arxiv created 2011/06/16 · openalex publication_date 2011/07/15 · arxiv updated 2012/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Reduced density-matrix functional theory (RDMFT) has become an appealing alternative to density-functional theory to describe electronic properties of strongly correlated systems. Here we derive exact conditions for the suitability of RDMFT to describe the two-dimensional homogeneous electron gas, which is the base system for semiconductor quantum dots and quantum Hall devices, for example. Following the method of Cioslowski and Pernal [J. Chem. Phys. 111, 3396 (1999)] we focus on the properties of power functionals of the form f(n,n^\ensuremath')=(nn^\ensuremath')^\ensuremathα for the scaling function in the exchange-correlation energy. We show that in order to have stable and analytic solutions, and for f to satisfy the homogeneous scaling constraint, the power is restricted to 1/4\ensuremath\leqslant\ensuremathα\ensuremath\leqslant3/4. Applying a reasonable ansatz for the momentum distribution and the lower bound for the exchange-correlation energy tightens the physical regime further to 0.64\ensuremath\lesssim\ensuremathα\ensuremath\leqslant0.75.