Discrete symmetry breaking defines the Mott quartic fixed point

Abstract

Because Fermi liquids are inherently non-interacting states of matter, all electronic levels below the chemical potential are doubly occupied. Consequently, the simplest way of breaking the Fermi-liquid theory is to engineer a model in which some of those states are singly occupied, keeping time-reversal invariance intact. We show that breaking an overlooked¹ local-in-momentum space ${{\mathbb{Z}}}_{2}$ symmetry of a Fermi liquid does precisely this. As a result, although the Mott transition from a Fermi liquid is correctly believed to arise without breaking any continuous symmetry, a discrete symmetry is broken. This symmetry breaking serves as an organizing principle for Mott physics whether it arises from the tractable Hatsugai–Kohmoto model or the intractable Hubbard model. Through a renormalization-group analysis, we establish that both are controlled by the same fixed point. An experimental manifestation of this fixed point is the onset of particle–hole asymmetry, a widely observed^{2,3,4,5,6,7,8,9,10} phenomenon in strongly correlated systems. Theoretically, the singly occupied region of the spectrum gives rise to a surface of zeros of the single-particle Green function, denoted as the Luttinger surface. Using K-homology, we show that the Bott topological invariant guarantees the stability of this surface to local perturbations. Our proof demonstrates that the strongly coupled fixed point only corresponds to those Luttinger surfaces with co-dimension p + 1 with odd p. We conclude that both Hubbard and Hatsugai–Kohmoto models lie in the same high-temperature universality class and are controlled by a quartic fixed point with broken ${{\mathbb{Z}}}_{2}$ symmetry.