Proof of a Stable Fixed Point for Strongly Correlated Electron Matter

Abstract

We establish the Hatsugai-Kohmoto model as a stable quartic fixed point (distinct from Wilson-Fisher) by computing the $\beta-$function in the presence of perturbing local interactions. In vicinity of the half-filled doped Mott state, the $\beta-$function vanishes for all local interactions regardless of their sign. The only flow away from the HK model is through the superconducting channel which lifts the spin degeneracy as does any ordering tendency. The superconducting instability is identical to that established previously\cite{nat1}. A corollary of this work is that Hubbard repulsive interactions flow into the HK stable fixed point in the vicinity of half-filling. Consequently, although the HK model has all-to-all interactions, nothing local destroys it. The consilience with Hubbard arises because both models break the $Z_2$ symmetry on a Fermi surface, the HK model being the simplest to do so. Indeed, the simplicity of the HK model belies its robustness and generality.