Mott Insulator & Hubbard Model
H = -t∑c†c + U∑n↑n↓ — correlation-driven metal-insulator transition
Spectral Function A(ω) — Density of States
Phase Diagram (U/t vs T/t) at half-filling
Double Occupancy ⟨n↑n↓⟩ vs U/t
Lattice Visualization
Hubbard Model: H = -t∑_{⟨ij⟩,σ} c†_{iσ}c_{jσ} + U∑_i n_{i↑}n_{i↓}. Two competing terms: t (hopping, kinetic energy, favors metallic state) and U (on-site Coulomb repulsion, favors localization).
Mott transition: At half-filling (one electron per site), when U ≫ t, each site is singly occupied. Adding an electron costs energy U (doublon formation) — a Mott gap opens. The spectral function splits into a lower Hubbard band (LHB) and upper Hubbard band (UHB) separated by U.
Quasiparticle weight Z: In the metallic phase, Z = (1 - U/U_c)^1 near the transition within Brinkman-Rice theory. At U=U_c ≈ 16t/3, Z→0 and the effective mass m*/m = 1/Z → ∞. The Fermi liquid collapses.
DMFT (Dynamical Mean Field Theory): The exact solution maps the lattice onto a self-consistent single-site impurity model. It captures the three-peak structure: LHB + quasiparticle peak + UHB. The transition is first-order at finite T.