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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 ℤ2 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 observed2,3,4,5,6,7,8,9,10 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 fixedmore »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 ℤ2 symmetry.« less

Even the particle world is not immune to identity politics. Bosons have been in a bit of an identity crisis, or so it has seemed since 1989 ( 1 ). Quantum mechanics requires bosons made of two paired electrons to either condense into a superfluid with a well-defined phase with zero electrical resistance or localize in an insulating state with infinite resistance. The direct transition from superconducting to insulating states was widely observed in a range of thin films ( 2 – 4 ). The most popular model for explaining these observations ( 5 ) claims that the destruction of superconductivity occurs when the resistance of the thin film exceeds a critical value. For bosons on the brink of localization, electrically insulating behavior is observed if the resistance is greater than the quantum of resistance, R q = h /4 e 2 , otherwise superconductivity persists, where h is Planck's constant and e is the electric charge. On page 1505 of this issue, Yang et al. ( 6 ) offer a counterexample by establishing that a bosonic metallic phase disrupts the superconductor-insulator transition (SIT) in the high-temperature superconductor YBa 2 Cu 3 O 7– x (YBCO).