Bose-Hubbard model
= Bose-Hubbard model
{c}
{title2=$H=-\sum_{ij}t_{ij}a_i^\dagger a_j+\tfrac U2\sum_i n_i(n_i-1)-\mu\sum_i n_i$}
A lattice <boson> <Hamiltonian operator> combining hopping and on-site repulsion. The on-site interaction counts distinct particle pairs through $n_i(n_i-1)/2$. It is the bosonic counterpart of the <Hubbard model>; projecting a continuum <contact interaction> onto localized <orbitals> gives $U=g\int|\varphi_i|^4$ when intersite overlaps are negligible.