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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:

Magnetic field driven insulator to metal transition

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)?

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While I do not have the knowledge to respond to your question in great detail, I can provide a simple plausibility argument if you mean for the Mott insulating phase to exist as a consequence of weak-localization.

Applying a magnetic field destroys the phase coherence that is necessary for producing the interference terms that affect charge transport.

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