Site dilution in the half-filled one-band Hubbard model: Ring exchange, charge fluctuations, and application toLa2Cu1−x(Mg/Zn)xO4

Abstract

We study the ground-state quantum spin fluctuations around the N\'eel ordered state for the one-band $(t,U)$ Hubbard model on a site-diluted square lattice. An effective spin Hamiltonian ${H}_{s}^{(4)}$ is generated using the canonical transformation method, expanding to order $t{(t/U)}^{3}$. ${H}_{s}^{(4)}$ contains four-spin ring exchange terms as well as second- and third-neighbor bilinear spin-spin interactions. Transverse spin fluctuations are calculated to order $1/S$ using a numerical real-space algorithm first introduced by Walker and Walstedt [Phys. Rev. B 22, 3816 (1980)]. Additional quantum charge fluctuations appear to this order in $t/U$, coming from electronic hopping and virtual excitations to doubly occupied sites. The ground-state staggered magnetization on the percolating cluster decreases with site dilution $x$, vanishing very close to the percolation threshold. We compare our results in the Heisenberg limit, $t/U\ensuremath{\rightarrow}0$, with quantum Monte Carlo (QMC) results on the same model and confirm the existence of a systematic $x$-dependent difference between $1/S$ and QMC results away from $x=0$. For finite $t/U$, we show that the effects of both the ring exchange and charge fluctuations die away rapidly with increasing $t/U$. We use our finite $t/U$ results to make a comparison with results from experiments on ${\text{La}}_{2}{\text{Cu}}_{1\ensuremath{-}x}{(\text{Mg}/\text{Zn})}_{x}{\text{O}}_{4}$.