  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.
