Constraints and topological order in the fermionic dimer model

The observed incompressible electronic phases at fractional lattice filling in moire structures have been interpreted as Wigner-Mott insulators. Here we explore the possibility that - with increasing quantum fluctuations - the charge order melts within the insulator resulting in a phase with fractionalized electrons. We establish some general constraints on such fractionalized electronic insulators. Armed with this theoretical understanding we numerically probe fermionic dimer models at fractional filling by performing exact diagonalization studies up to 126 sites.