Bose-Hubbard in optical lattice: H = -J·Σ b†b + (U/2)·Σ n(n-1) in tensor-product site basis

Bose-Hubbard model on an optical lattice. Setup: neutral atoms loaded into a standing-wave potential V(x) = V₀·sin²(k·x) forming an array of micro-traps. In the tight-binding limit (V₀ ≫ E_recoil) the single-particle Hilbert space…