Hubbard Model
H = -t Σ c†ᵢσcⱼσ + U Σ nᵢ↑nᵢ↓
Mott transition at U_c ≈ W (half-filling)
Metal: U < W — free hopping, Fermi liquid
Mott insulator: U > W — localized spins, charge gap = U-W
Quasiparticle weight:
Z = 1 - (U/U_c)² for U < U_c
State: —
Charge gap: —
Z = —
H = -t Σ c†ᵢσcⱼσ + U Σ nᵢ↑nᵢ↓
Mott transition at U_c ≈ W (half-filling)
Metal: U < W — free hopping, Fermi liquid
Mott insulator: U > W — localized spins, charge gap = U-W
Quasiparticle weight:
Z = 1 - (U/U_c)² for U < U_c
State: —
Charge gap: —
Z = —