The exceptional origin of the strange metal and the LFL-HFL transition

Abstract

We propose an algebraic framework for the strange metal regime of strongly correlated electrons. We show that the exceptional superconformal algebra $D(2,1;\alpha)$ admits two distinct contractions of its conformal sector: one to a pair of canonical fermions, the underlying degrees of freedom of the Landau--Fermi liquid (LFL), and one to the algebra of Hubbard operators, which characterise a distinct metallic regime, the Hubbard--Fermi liquid (HFL). We argue that competition between these two metallic states drives the emergence of the strange metal as a $0+1$D superconformal bath. We analyse the resulting thermodynamics, and at leading order obtain a parameter-free prediction, $4\pi^2\gamma^{-1} =\chi_s^{-1} + \chi_c^{-1}$, relating the Sommerfeld coefficient to the static spin and charge susceptibilities. We further show that the LFL-HFL transition is discontinuous at low temperature, forced by an algebraic constraint on the Hubbard contraction, and map out the resulting phase diagram. We connect the framework to microscopic lattice models and to the phenomenology of correlated insulators.