Discrete symmetry breaking defines the Mott quartic fixed point

Because Fermi liquids are inherently non-interacting states of matter, all electronic levels below the chemical potential doubly occupied. Consequently, simplest way breaking liquid theory is to engineer a model in which some those singly occupied keeping time-reversal invariance intact. We show that an overlooked local-in-momentum space $\mathbb Z_2$ symmetry does precisely this. As result, while Mott transition from correctly believed obtain without any continuous symmetry, discrete broken. This serves as organizing principle for physics whether it arises tractable Hatsugai-Kohmoto (HK) or intractable Hubbard model. That both controlled by same fixed point we establish through renormalization group analysis. An experimental manifestation this onset particle-hole asymmetry, widely observed phenomenon strongly correlated systems. Theoretically, singly-occupied region spectrum gives rise surface zeros single-particle Green function, denoted Luttinger surface. Using K-homology, Bott topological invariant guarantees stability local perturbations. Our proof demonstrates coupled only corresponds surfaces with co-dimension $p+1$ $p$ odd. conclude and HK models lie high temperature universality class broken quartic point.