A simple model for strange metallic behaviour
We show how strange metallic behavior emerges from a simple effective semi-holographic theory with only two couplings. This model is justified by the Wilsonian RG approach but ignores order parameters, and describes carrier electrons interacting with a critical sector with only two effective dimensionless couplings. We establish that this model has an emergent universal spectral function near the Fermi surface at an optimal ratio of the two effective couplings when the critical exponent ν lies between 0.66 and 0.95 for a wide range of temperatures which could be as low as 1 percent of the Fermi energy when ν is at the higher end. The linear in T resistivity and quadratic in T Hall resistivity (the latter for a spherical Fermi surface) follow from the universality of the spectral function for a wide range of temperatures in which the relevant loop integrals get contributions mainly from momenta near the Fermi surface. Our spectral functions fit very well with data from ARPES experiments for optimal, over and under-doping with a fixed exponent over a range of temperatures, validating universality at optimal doping. We obtain a refined Planckian dissipation picture where the scattering time τ≈f⋅ℏ/(kBT) with f almost independent of all model parameters except for the overall strength of the two couplings when their ratio is optimal. We find f≈1 when the couplings take maximal value for which strange metallic behavior is exhibited. However, f≈10 when the couplings are smaller. Although not derivable from quasi-particles, our results at optimal doping fit a Drude-type phenomenology with Planckian scattering time, and an almost model-independent n/m, which is about 2π times the Fermi liquid value at same EF.