Monte Carlo Study of Three-dimensional Flat-Band Ferromagnetism in a Diamond Lattice

We study the p-orbital bands in the orbital-active diamond lattice. This system features doubly-degenerate flat bands at each momentum in the Brillouin zone as well as dispersive bands exhibiting nodal-line semimetal behavior. Due to the suppression of kinetic energy, strong correlation effects lead to ferromagnetism in the flat bands, which can be mapped to a modified percolation problem. We investigate the transition between the paramagnetic and ferromagnetic phases in the flat bands via Monte Carlo simulation.