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Accepted · first revision · record

Title: Critical density for Wigner crystallization of the clean 2D electron gas
Plain: Computer simulations predict the electron sheet crystallizes once repulsion exceeds kinetic energy by a factor of roughly 30 to 40, but the exact threshold and whether the change is abrupt are not pinned down.
Precise: For the 2D homogeneous electron gas with $1/r$ repulsion and a uniform neutralizing background at $T = 0$, determine the critical r_s_c for the liquid to triangular Wigner crystal transition, whether it is first order, and the spin state of each phase. Diffusion Monte Carlo gave r_s_c ~ 37 (Tanatar and Ceperley 1989), $31 \pm 1$ (Drummond and Needs 2009) and $35 \pm 1$ with no stable ferromagnetic fluid (Azadi, Drummond and Vinko 2024, Physical Review B 110, 245145); an answer is r_s_c with controlled fixed-node and finite-size errors.
Settled by: A calculation with controlled nodal error (for example neural-network variational wavefunctions benchmarked against released-node or auxiliary-field results) at sizes that allow a thermodynamic extrapolation.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: open
Status note: Fixed-node diffusion Monte Carlo estimates differ by more than their quoted errors ($31 \pm 1$ in 2009, $35 \pm 1$ in 2024), so nodal and finite-size errors are not under control.
Posed since: (empty)