Marginal Fermi Liquid — Varma Self-Energy
Im Σ(ω,T) ~ max(|ω|,T) — no quasiparticle pole, logarithmic optical conductivity
Varma's Marginal Fermi Liquid (1989): the bosonic spectrum P(ω,T) ∝ T/ω (|ω|≪T), 1 (|ω|≫T) gives Im Σ ~ −λmax(|ω|,T) and Re Σ ~ λω ln(ω_c/max(|ω|,T)). The spectral function has no sharp quasiparticle peak — Z→0 logarithmically. Optical conductivity σ₁(ω) ∝ (1/ω)ln(ω_c/ω), explaining anomalous mid-IR absorption in cuprates.