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

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') = (nn')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