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It is indeed possible to change between these phases adiabatically. Since, as you noted, the ground state changes between being a superfluid and a Mott insulator, starting in the ground state and making an adiabatic change means that you track that change in state by definition. Note that this diagram is only formally true for the Grand Canonical ensemble, ...

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Collected Papers of L.D. Landau edited by D. Ter Haar The Discovery of Super Fluidity These above books might help you. Start doing your own research, this is how we study.

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An ideal gas or near-ideal gas such as air at about atmospheric pressure and room temperature has a bulk modulus which is the same as its pressure. That can be readily confirmed by taking the ideal gas equation $PV=nRT$ and substituting it into the equation for the bulk modulus $B=-V \frac{dP}{dV}$. Now for what P-V equations-of-state does the bulk modulus ...

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The Landau criterion is not in itself a criterion for superfluidity, but a criterion for the breakdown of superfluidity. Indeed, if applied to insulators or ordinary fluids, it would tell you that all of these are also superfluid... What the Landau criterion tells you is the velocity of the superfluid flow at which excitations are created from the ...

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