The Hubbard model H = −t Σ c†c + U Σ n↑n↓ captures the competition between kinetic energy (bandwidth W≈8t) and on-site repulsion U. At half-filling, a Mott insulator forms when U exceeds a critical value U_c≈W. The spectral function develops a gap, splitting the band into lower and upper Hubbard bands separated by U.
Hubbard Hamiltonian:
H = −t Σ c†c + U Σ n↑n↓ − μN
Half-bandwidth: D = 4t (square lat.)
Mott criterion: U_c ≈ W = 2D
Spectral weight A(ω):
Metal: quasiparticle peak at ω=0
Insulator: gap = U − W opens
DMFT result (T=0):
U_c1 ≈ 2.39D (insulator→metal)
U_c2 ≈ 2.92D (metal→insulator)
Hysteresis between U_c1 and U_c2