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A phase transition is a change in the nature of a phase or in the number of phases of a system as a result of a change in the external conditions. Examples: melting/freezing, vaporization/condensation, ferromagnetic transition, superconducting transition.
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Why does $[H,N]=0$ violate with superfluid phase judgement $\left<b\right>=0?$
I'm working with the standard Boson Hubbard model. It's Hamiltonian is defined in Fock space and commutes with total particle number N.
$$[{{\hat H}_{BH}},\hat N] = 0$$
So I can simultaneously diagno …