Phase Diagram of the Low-Density Two-Dimensional Homogeneous Electron Gas

TL;DR

This study uses quantum Monte Carlo simulations to map the phase diagram of the two-dimensional electron gas at zero temperature, identifying phase transitions between fluid and crystal states with different magnetic properties.

Contribution

It provides the first detailed quantum Monte Carlo phase diagram for the 2D electron gas, including precise transition points and ruling out a previously proposed hybrid phase.

Findings

Transition from paramagnetic fluid to antiferromagnetic Wigner crystal at r_s=31(1) a.u.

Transition to ferromagnetic crystal at r_s=38(5) a.u.

Fully spin-polarized fluid is never stable.

Abstract

We have used quantum Monte Carlo methods to calculate the zero-temperature phase diagram of the two-dimensional homogeneous electron gas. We find a transition from a paramagnetic fluid to an antiferromagnetic triangular Wigner crystal at density parameter r_s=31(1) a.u. and a transition to a ferromagnetic crystal at r_s=38(5) a.u. The fully spin-polarized fluid is never stable. We searched for, but did not find, the ferromagnetic hybrid phase proposed by H. Falakshahi and X. Waintal [Phys. Rev. Lett. 94, 046801 (2005)].