Uniform quantized electron gas

TL;DR

This paper investigates the correlation energy of a uniform electron gas at zero temperature using classical statistical mechanics methods, interpreting the quantum problem as a classical polymer system in imaginary time.

Contribution

It introduces a modified RPA that enforces the Pauli exclusion principle for electrons with equal spins, improving correlation energy calculations.

Findings

Recovered the RPA using classical fluid methods

Developed a modified RPA respecting electron spin exclusion

Numerical results agree with Monte Carlo data

Abstract

In this work we study the correlation energy of the quantized electron gas of uniform density at temperature $T=0$. To do so we utilize methods from classical statistical mechanics. The basis for this is the Feynman path integral for the partition function of quantized systems. With this representation the quantum mechanical problem can be interpreted as, and is equivalent to, a classical polymer problem in four dimensions where the fourth dimension is imaginary time. Thus methods, results, and properties obtained in the statistical mechanics of classical fluids can be utilized. From this viewpoint we recover the well known RPA (random phase approximation). Then to improve it we in this work modify the RPA by requiring the corresponding correlation function to be such that electrons with equal spins can not be on the same position. Numerical evaluations are compared with well known results of a standard parameterization of Monte Carlo correlation energies.