Hubbard model

A lattice fermion model combining hopping with local density interaction, conventionally written $U_H{\sum }_n{n}_{n\uparrow }{n}_{n\downarrow }$. Its interaction parameter must be matched when a spin-square representation is used: $-2U({\mathbf{S}}^2-3n/4)$ equals $3U{n}_{\uparrow }{n}_{\downarrow }$, so $U_H=3U$ for that representation.