6533b826fe1ef96bd1283eb5
RESEARCH PRODUCT
Constraints of reduced density-matrix functional theory for the two-dimensional homogeneous electron gas
Esa RäsänenA. Putajasubject
Physicsta114Strongly Correlated Electrons (cond-mat.str-el)Order (ring theory)FOS: Physical sciencesQuantum Hall effectCondensed Matter PhysicsUpper and lower boundsElectronic Optical and Magnetic MaterialsBase (group theory)Condensed Matter - Strongly Correlated ElectronsQuantum mechanicsFermi gasScalingEnergy (signal processing)Ansatzdescription
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 $f(n,{n}^{\ensuremath{'}})={(n{n}^{\ensuremath{'}})}^{\ensuremath{\alpha}}$ 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 $1/4\ensuremath{\leqslant}\ensuremath{\alpha}\ensuremath{\leqslant}3/4$. Applying a reasonable ansatz for the momentum distribution and the lower bound for the exchange-correlation energy tightens the physical regime further to $0.64\ensuremath{\lesssim}\ensuremath{\alpha}\ensuremath{\leqslant}0.75$.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-01-01 |