Néel order, ring exchange, and charge fluctuations in the half-filled Hubbard model

Abstract

We investigate the ground state properties of the two-dimensional half-filled one band Hubbard model in the strong (large-$U$) to intermediate coupling limit (i.e., away from the strict Heisenberg limit) using an effective spin-only low-energy theory that includes nearest-neighbor exchange, ring exchange, and all other spin interactions to order $t{(t∕U)}^{3}$. We show that the operator for the staggered magnetization, transformed for use in the effective theory, differs from that for the order parameter of the spin model by a renormalization factor accounting for the increased charge fluctuations as $t∕U$ is increased from the $t∕U\ensuremath{\rightarrow}0$ Heisenberg limit. These charge fluctuations lead to an increase of the quantum fluctuations over and above those for an $S=1∕2$ antiferromagnet. The renormalization factor ensures that the zero temperature staggered moment for the Hubbard model is a monotonously decreasing function of $t∕U$, despite the fact that the moment of the spin Hamiltonian, which depends on transverse spin fluctuations only, in an increasing function of $t∕U$. We also comment on quantitative aspects of the $t∕U$ and $1∕S$ expansions.