  Two-dimensional moire superlattices have recently emerged as a fertile ground
for creating novel electronic phases of matter with unprecedented control.
Despite intensive efforts, theoretical investigation of correlated moire
systems has been challenged by the large number of atoms in a superlattice unit
cell and the inherent difficulty of treating electron correlation. The physics
of correlated moire systems is governed by low-energy electrons in a
coarse-grained long-wavelength potential, unlike the singular Coulomb potential
of atomically-spaced ions in natural solids. Motivated by the separation
between moire and atomic length scales, in this work we apply density
functional theory to study directly the continuum model of interacting
electrons in the periodic moire potential. Using this quantitatively accurate
method, we predict itinerant spin-valley ferromagnetism in transition metal
dichalchogenide heterobilayers, which originates from the constructive
interplay between moire potential and Coulomb interaction in a two-dimensional
electron system.
