Study of Simulation Cell Size in Mean-Field Studies of Interacting Lattice Models (Communications in Computational Physics, 2018)
A lattice model of interacting fermions is studied with the principal aimof assessing the dependence of calculated mean-field ground states versus the N×N lattice size, with N=16, 32, and 48. A two band model on the two-dimensionalsquare lattice is simulated, with on-site energies and interaction parameters chosento represent crystal field split orbitals in the moderately correlated regime. Nearestneighbor hopping leads to the well known van Hove singularities (vHs) of the squarelattice. Anomalies in the inverse participation ratio of the eigenstates are found to beassociated with the vHs, with their prevalence decreasing inversely with N. For thechosen model, inhomogeneous spin densities are always obtained for the small latticesize N=16, with the degree of variation decreasing rapidly for most polarizations as Nis increased. Various spin polarizations are treated, and one case in which spin densityinhomogeneity persists for the largest lattice size is discussed and analyzed. Couplingof spin density inhomogeneities to charge density variation is minor but evident, andis primarily of intra-orbital origin.
Keywords: Lattice Hamiltonian; mean field; lattice size; moderate interactions.