Topology of the Fermi surface and universality of the metal-metal and metal-insulator transitions: $d$-dimensional Hatsugai-Kohmoto model as an example

The earlier theory [1] of the quantum phase transitions related to the change of the Fermi Surface Topology (FST) is advanced. For such transitions the Fermi surface as a quantum critical manifold determined by the Lee-Yang zeros, the order parameter $\mathcal{P}$ as the $d$-volume of the Fermi sea,