MOTT-HUBBARD TRANSITION

Correlation-driven metal-insulator transition

U/t (interaction/hopping) 2.0

Filling n 1.0

Temperature T/t 0.1

PHASE

METAL

Quasiparticle weight Z—

Double occupancy D—

U_c / t (Brinkman-Rice)~8 (D=∞)

H = -t Σ c†ᵢσcⱼσ + U Σ nᵢ↑nᵢ↓ - μ Σ nᵢ

At half-filling (n=1), increasing U/t drives a transition from a Fermi liquid metal to a Mott insulator where electrons are localized by Coulomb repulsion. The quasiparticle weight Z → 0 signals diverging effective mass. Brinkman-Rice (1970) gives Z = 1-(U/U_c)² via Gutzwiller.