Mott-Hubbard Transition — Spectral Weight Transfer

H = −t Σ c†ᵢσcⱼσ + U Σ nᵢ↑nᵢ↓. As U/W increases (W=bandwidth), the spectral function A(ω) transfers weight from the quasiparticle peak at ω=0 to Hubbard bands at ω≈±U/2. Brinkman-Rice: Z = 1 − (U/U_c)² → 0 at U_c, m*/m = 1/Z → ∞. DMFT gives U_c ≈ 2.94W for the half-filled Bethe lattice. Above U_c, a Mott gap Δ ≈ U − W opens; below, a Fermi liquid with enhanced mass forms.