Ground state phases of the two-dimension electron gas with a unified variational approach

TL;DR

This paper introduces a unified variational approach using neural quantum states to study the 2D electron gas, revealing lower energies and a phase transition at lower densities than previously thought, with evidence of intermediate states.

Contribution

It presents a novel neural network-based variational ansatz that unifies the description of all phases of the 2DEG and improves upon existing energy estimates.

Findings

Transition to Wigner crystal at rs = 37 +/- 1

Lower ground-state energies than previous methods

Evidence for intermediate phases with nematic correlations

Abstract

The two-dimensional electron gas (2DEG) is a fundamental model, which is drawing increasing interest because of recent advances in experimental and theoretical studies of 2D materials. Current understanding of the ground state of the 2DEG relies on quantum Monte Carlo calculations, based on variational comparisons of different ansatze for different phases. We use a single variational ansatz, a general backflow-type wave function using a message-passing neural quantum state architecture, for a unified description across the entire density range. The variational optimization consistently leads to lower ground-state energies than previous best results. Transition into a Wigner crystal (WC) phase occurs automatically at rs = 37 +/- 1, a density lower than currently believed. Between the liquid and WC phases, the same ansatz and variational search strongly suggest the existence of intermediate states in a broad range of densities, with enhanced short-range nematic spin correlations.