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We study the ground state phase diagram of the degenerate two-band Hubbard model at integer fillings as a function of onsite Hubbard interaction U and Hund’s exchange coupling J. We use a variational slave-spin mean field method which allows symmetry broken states to be studied within the computationally less intensive slave-spin mean field formalism. The results show that at half-filling, the ground state at smaller U is a Slater antiferromagnet with substantial local charge fluctuations. As U is increased, the antiferromagnetic (AF) state develops a Heisenberg behavior, finally undergoing a first-order transition to a Mott insulating AF state at a critical interaction U c which is of the order of the bandwidth. Introducing the Hund’s coupling J correlates the system more and reduces U c drastically. At quarter-filling with one electron per site, the ground state at smaller U is paramagnetic metallic. At finite J, as interaction is increased beyond a lower critical value U c1, it goes to a fully spin polarized ferromagnetic state coexisting with an antiferro-orbital order. Further increase in U beyond a higher critical value U c2 results in the Mott insulating state where local charge fluctuation vanishes.

We study the ground state of the three-band degenerate Hubbard model on a square lattice at integer fillings using the variational slave-spin mean field method. At half-filling, the method reproduces the well known result that the ground state is antiferromagnetic (AF) insulating at smaller values of Hubbard onsite repulsion U, while it becomes Mott insulating with Néel AF order at higher U. Away from half-filling, for two particles per site, we show that the model supports a ferromagnetic (FM) metallic state with fully polarized spins at sufficiently large U. The FM state occurs irrespective of the value of Hund’s coupling J. The ferromagnetism at J = 0 can be explained by the Stoner mechanism while that for J > 0 is shown to arise from the superexchange process. At this band filling, the Hund’s coupling J is known to have the Janus-faced effect on electronic correlations where it enhances correlations at smaller U while reducing it at higher U. We show that these two effects are separated by the paramagnetic (PM) to FM transition point. The former effect is obtained at the PM state while the latter occurs in the FM state. The FM phase also occurs for one particle per site but here Hund’s coupling J reduces the effect of electronic correlations at all U.

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