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A general multi-orbital Hubbard model, which includes on-site inter-orbitalelectron hoppings, is introduced and studied. It is shown that the on-siteinter-orbital single electron hopping is one of the most basic interactions.Two electron spin-flip and pair-hoppings are shown to be correlation effects ofhigher order than the on-site inter-orbital single hopping. It is shown how thedouble and higher hopping interactions can be well-defined for arbitrarysystems. The two-orbital Hubbard model is studied numerically to demonstratethe influence of the single electron hopping effect, leading to a change of theshape of the bands and a shrinking of the difference between the two bands.Inclusion of the on-site inter-orbital hopping suppresses the so-calledorbital-selective Mott transition.

Investigation of on-site inter-orbital single electron hoppings in general multi-orbital systems