Analytic theory of correlation energy and spin polarization in the 2D electron gas

TL;DR

This paper develops an analytic model for the correlation energy and spin polarization in a 2D electron gas, accurately matching quantum Monte Carlo data and identifying a quantum phase transition at a specific coupling strength.

Contribution

It introduces a novel analytic approach solving a scattering Schrödinger equation with an effective potential, incorporating exchange, kinetic, and correlation effects, to describe the 2D electron gas.

Findings

Excellent agreement with quantum Monte Carlo data.

Identification of a quantum phase transition at r_s ≈ 24.

Accurate prediction of correlation energy and spin polarization.

Abstract

We present an analytic theory of the pair distribution function and the ground-state energy in a two-dimensional (2D) electron gas with an arbitrary degree of spin polarization. Our approach involves the solution of a zero-energy scattering Schr\"odinger equation with an effective potential which includes a Fermi term from exchange and kinetic energy and a Bose-like term from Jastrow-Feenberg correlations. The form of the latter is assessed from an analysis of data on a 2D gas of charged bosons. We obtain excellent agreement with data from quantum Monte Carlo studies of the 2D electron gas. In particular, our results for the correlation energy show a quantum phase transition occurring at coupling strength $r_s\approx 24$ from the paramagnetic to the fully spin-polarized fluid.