Site Dilution in the Half-Filled One-Band Hubbard Model: Ring Exchange, Charge Fluctuations and Application to La2Cu_{1-x}(Mg/Zn)_xO4

TL;DR

This paper investigates quantum spin fluctuations, charge effects, and site dilution in the Hubbard model, providing insights into magnetic properties and comparing theoretical results with experiments on doped cuprates.

Contribution

The study derives an effective spin Hamiltonian including ring exchange and charge fluctuations, analyzing their effects on magnetic order in site-diluted Hubbard models.

Findings

Magnetization decreases with site dilution, vanishing near percolation threshold.

Ring exchange and charge fluctuations diminish rapidly as t/U increases.

Results align with quantum Monte Carlo and experimental data on doped cuprates.

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, $H_{\rm s}^{(4)}$, is generated using the canonical transformation method, expanding to order $t(t/U)^3$. $H_{\rm s}^{(4)}$ 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 Walsteadt. 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, $t/U \to 0$, 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 La$_2$Cu$_{1-x}$(Mg/Zn)$_x$O$_4$.