I want to ask the underlying reason for the destruction of Mott insulating phase by an external magnetic field. I know that for a normal band insulator, the transition to a metallic phase can be explained by a shifting of band energy $\Delta E\sim g\mu_B B$ due to spin (neglecting the orbital effect). As shown in the schematic below:
However, what about the Mott insulator, I have seen some people also trying to use this kind of argument to explain the transition from a Mott insulator to a metal, but why this is true? What if the magnetic field "does" something on the ground state itself? Can we still use $g\mu_B B$ as a measure of the "gap" of the Mott insulator (by "gap" here I mean things like the gap between upper and lower Hubbard band)?