Competing roles of longitudinal and transverse Hund's terms on Mott transitions

Effects of longitudinal (JZ) and transverse (including spin-flip JX and pair-hopping JP terms) Hund's couplings on Mott transitions of two-orbital Hubbard models are studied by the rotationally invariant slave boson approach. We show that in the half-filled asymmetric systems, the orbital selective Mott phase (OSMP) expands with increasing JX,P/JZ when JX,P/JZ<1, and has the largest region in the isotropic case (JX,P/JZ=1); and further increasing spin-flip Hund's coupling to JX,P/JZ>1 may quickly suppress the OSMP state. In other near-half-filled systems, the transverse Hund's coupling favors or unfavors the OSMP state, depending on the electronic correlation strength of the systems. In the quarter-filled and around systems, a small JX,P/JZ<1 has less effect on Mott transition, while a large JX,P/JZ>1 enhances the electron itineracy and considerably increases the critical correlation strength of the Mott transition both in symmetric and asymmetric systems. These results could be addressed by different spin-orbital states favored by JX, JP and JZ components, respectively; and the competing longitudinal and transverse Hund's coupling terms lead to most strong quantum fluctuations in the isotropic system.