Bose-Hubbard Model — Superfluid / Mott Insulator Phase Diagram

Temperature T/U: 0.01 Max Mott lobes: 4 Animate T

Click diagram to probe phase | —

The Bose-Hubbard model H = -J∑(a†a) + (U/2)∑n(n-1) - μ∑n has a quantum phase transition between Mott insulator (integer filling, gapped) and superfluid (coherent, compressible) phases. Mott lobes appear in the (J/U, μ/U) plane for each integer occupation n.