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Because Fermi liquids are inherently non-interacting states of matter, allelectronic levels below the chemical potential are doubly occupied.Consequently, the simplest way of breaking Fermi liquid theory is to engineer amodel in which some of those states are singly occupied keeping time-reversalinvariance intact. We show that breaking an overlooked local-in-momentum space$\mathbb Z_2$ symmetry of a Fermi liquid does precisely this. As a result,while the Mott transition from a Fermi liquid is correctly believed to obtainwithout the breaking of any continuous symmetry, a discrete symmetry is broken.This symmetry breaking serves as an organizing principle for Mott physicswhether it arises from the tractable Hatsugai-Kohmoto (HK) model or theintractable Hubbard model. That both are controlled by the same fixed point weestablish through a renormalization group analysis. An experimentalmanifestation of this fixed point is the onset of particle-hole asymmetry, awidely observed phenomenon in strongly correlated systems. Theoretically, thesingly-occupied region of the spectrum gives rise to a surface of zeros of thesingle-particle Green function, denoted as the Luttinger surface. UsingK-homology, we show that the Bott topological invariant guarantees thestability of this surface to local perturbations. Our proof demonstrates thatthe strongly coupled fixed point only corresponds to those Luttinger surfaceswith co-dimension $p+1$ with $p$ odd. We conclude that the Hubbard and HKmodels both lie in the same high temperature universality class and arecontrolled by the broken $\mathbb Z_2$ symmetry quartic fixed point.

Doped Mott Insulators Break $\mathbb Z_2$ Symmetry of a Fermi Liquid: Stability of Strongly Coupled Fixed Points