Ising Expansion for the Hubbard Model

Abstract

We develop series expansions for the ground state properties of the Hubbard model, by introducing an Ising anisotropy into the Hamiltonian. For the two-dimensional (2D) square lattice half-filled Hubbard model, the ground state energy, local moment, sublattice magnetization, uniform magnetic susceptibility and spin stiffness are calculated as a function of $U/t$, where $U$ is the Coulomb constant and $t$ is the hopping parameter. Magnetic susceptibility data indicate a crossover around $U\approx 4$ between spin density wave antiferromagnetism and Heisenberg antiferromagnetism. Comparisons with Monte Carlo simulations, RPA result and mean field solutions are also made.