Constraints of reduced density-matrix functional theory for the two-dimensional homogeneous electron gas

Abstract

Reduced density-matrix functional theory (RDMFT) has become an appealing alternative to density-functional theory to describe electronic properties of highly-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, e.g., semiconductor quantum dots and quantum Hall devices. Following the method of Cioslowski and Pernal [J. Chem. Phys. {\bf 111}, 3396 (1999)] we focus on the properties of power functionals of the form $f(n,n^{\prime })=(n{n}^{\prime }{)}^{\alpha }$ 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 $1/4\le \alpha \le 3/4$. Applying a reasonable ansatz for the momentum distribution and the lower bound for the exchange-correlation energy tightens the physical regime further to $0.64\lesssim \alpha \le 0.75$.

References in corpus (10)

• Reduced Density Matrix Functional for Many-Electron Systems
• Combining Density Functional Theory and Density Matrix Functional Theory
• Collapse of the Electron Gas to Two Dimensions in Density Functional Theory
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• Dimensional crossover of the exchange-correlation energy at the semilocal level
• Interaction-Induced Spin Polarization in Quantum Dots
• Density gradients for the exchange energy of electrons in two dimensions
• Parameter-free density functional for the correlation energy in two dimensions
• Reduced density-matrix functional theory in quantum Hall systems
• Laplacian-level density functionals for the exchange-correlation energy of low-dimensional nanostructures

Cited by in corpus (3)

• Spectral density and metal-insulator phase transition in Mott insulators within RDMFT
• Photoemission Spectra from Reduced Density Matrices: the Band Gap in Strongly Correlated Systems
• On the validity of power functionals for the homogeneous electron gas in reduced.density-matrix-functional theory