A model of a 2d non-Fermi liquid with SO(5) symmetry, AF order and a d-wave SC gap

Abstract

Demanding a consistent quantum field theory description of spin- particles near a circular Fermi surface in 2d leads to a unique fermionic theory with relevant quartic interactions which has an emergent Lorentz symmetry and automatically has an Sp(4) = SO(5) internal symmetry. The interacting theory has a low-energy interacting fixed point and is thus a non-Landau/Fermi liquid. Anti-ferromagnetic (AF) and superconducting (SC) order parameters are bilinears in the fields and form the five-dimensional vector representation of SO(5). An AF phase occurs at low doping which terminates in a first-order transition. We incorporate momentum-dependent scattering of Cooper pairs near the Fermi surface to 1-loop and derive a new kind of SC gap equation beyond mean field with a d-wave gap solution. Taking into account the renormalization group (RG) scaling properties near the low-energy fixed point, we calculate the complete phase diagram as a function of doping, which shows some universal geometric features. The d-wave SC dome terminates on the over-doped side at the fixed point of the RG, which is a quantum critical point. Optimal doping is estimated to occur just below 3/2π2. The critical temperature for SC at optimal doping is set mainly by the universal nodal Fermi velocity and lattice spacing, and is estimated to average around 140 K for LSCO. The pseudogap energy scale is identified with the RG scale of the coupling.