Landau-cutkosky rules, scale invariance, and the marginal fermi liquid

Abstract

With the aid of the reduced graph expansion relating different order multiple interaction vertices and the exact spectral densities, we show that a strongly coupled Fermi system can allow solutions for the spectral density which scale under simultaneous scale changes in the energy and temperature. This implies a functional form for the spectral density which falls off as a power μ of frequency between 0 and −1. The theory describes Z kF = 0 quasiparticles with a Fermi surface consistent with Luttinger's theorem while the spin and charge susceptibilities have imaginary parts of the form ( ω/ T) T 1+2 μ at low energies. The approach reproduces some features of both the Luttinger liquid and marginal Fermi liquid phenomenologies.