Ground-state energy of a high-density electron gas in a strong magnetic field

TL;DR

This paper analyzes the ground-state energy of a high-density electron gas subjected to a strong magnetic field, focusing on the quantum limit where only the lowest Landau level is occupied, and derives a perturbation series analogous to the field-free case.

Contribution

It introduces a new perturbation series for the ground-state energy in a strong magnetic field, replacing the traditional expansion parameter with a magnetic field-dependent one.

Findings

Perturbation series analogous to Gell-Mann Brueckner expression.

New expansion parameter $r_B$ for strong magnetic fields.

Ground-state energy can be expressed similarly to the field-free case.

Abstract

The high-density electron gas in a strong magnetic field B and at zero temperature is investigated. The quantum strong-field limit is considered in which only the lowest Landau level is occupied. It is shown that the perturbation series of the ground-state energy can be represented in analogy to the Gell-Mann Brueckner expression of the ground-state energy of the field-free electron gas. The role of the expansion parameter is taken by $r_B= (2/3 \pi^2) (B/m^2) (\hbar r_S/e)^3$ instead of the field-free Gell-Mann Brueckner parameter r_s.