Bose-Hubbard
⟨cos Δθ⟩: 0.000
Superfluid ρₛ: 0.000
Phase: ?
Critical J/U≈0.18
H = −J Σ cos(θᵢ−θⱼ) + (U/2) Σ n̂ᵢ². The competition between hopping J (superfluid) and on-site repulsion U (Mott insulator) drives a quantum phase transition at J/U ≈ 0.18 for the 2D square lattice. Phase coherence collapses at the Mott boundary.