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Accepted · first revision · record

Title: Correlation-length exponent of the 3D Anderson-Mott transition with Coulomb interaction
Plain: For electrons that do not repel, the transition exponent is known numerically to three digits. For real electrons, which repel through the Coulomb force, no reliable value exists.
Precise: For 3D disordered electrons with $1/r$ repulsion (Finkelstein nonlinear sigma model; with and without spin-orbit scattering or magnetic field), compute the correlation-length exponent $\nu$ and the dynamical exponent $z$ at the metal-insulator transition with controlled error, and compare with the non-interacting values $\nu \sim 1.57$ (orthogonal), $\sim 1.44$ (unitary) and $\sim 1.37$ (symplectic).
Settled by: A non-perturbative computation (self-consistent Hartree-Fock with exact diagonalization, functional renormalization group of the sigma model, or quantum Monte Carlo of a lattice model with Coulomb interaction) with finite-size scaling and error bars.
Kind: well-posed
Answer type: value
References: (empty)
Literature status: open
Status note: A density-functional (Kohn-Sham, mean-field) model of a doped semiconductor gave $\nu \sim 1.3$ (Harashima and Slevin, Physical Review B 89, 205108, 2014), suggesting a different universality class; no controlled many-body result exists.
Posed since: (empty)