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

TL;DR

This paper investigates the applicability of reduced density-matrix functional theory (RDMFT) to the two-dimensional homogeneous electron gas, deriving conditions on power functionals for stable and physical solutions relevant to quantum dots and Hall devices.

Contribution

It derives exact conditions for the use of RDMFT with power functionals in 2D electron gases, narrowing the parameter range for physically meaningful solutions.

Findings

Power functional exponent must be between 1/4 and 3/4 for stability.

Physical regime further constrained to approximately 0.64 to 0.75.

Provides theoretical bounds for RDMFT applicability in 2D systems.

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 $f(n,n')=(n n')^\alpha$ 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 $1/4 \leq \alpha \leq 3/4$. Applying a reasonable ansatz for the momentum distribution and the lower bound for the exchange-correlation energy tightens the physical regime further to $0.64 \lesssim \alpha \leq 0.75$.