Antiferromagnetism beyond classical percolation threshold in the site-diluted half-filled one-band Hubbard model in three dimensions

TL;DR

This study explores how antiferromagnetic order persists beyond the classical percolation threshold in a site-diluted Hubbard model, revealing the role of induced moments and the effects of interaction strength and temperature.

Contribution

It demonstrates that magnetic order can survive below the classical percolation threshold due to induced moments on non-interacting sites, a novel insight into disordered correlated systems.

Findings

Antiferromagnetic order persists below the classical percolation threshold due to induced moments.

The insulator-to-metal crossover temperature $T^*$ decreases rapidly with dilution, while $T_N$ remains stable initially.

Increasing $U$ or temperature suppresses induced moments and restores classical percolation behavior.

Abstract

We investigate the impact of site dilution by setting the on-site repulsion strength ($U$) to zero at a fraction of sites in the half-filled Hubbard model on a simple cubic lattice. We employ a semi-classical Monte-Carlo approach first to recover the zero dilution (undiluted $x=1$) properties, including $U$ dependence of insulator to metal crossover temperature scale $T^*$ and long-range staggered antiferromagnetic ordering temperature ($T_N$). For the non-perturbative regime of $U \sim$ bandwidth, we find a rapid suppression of $T^*$ with reducing $x$ from 1 to 0.7. However, $T_N$ remains unchanged in this dilution range, showing a weakening of the insulating state but not of the magnetic order. At $x \leq 0.7$, $T^*$ and $T_N$ coincide and are suppressed together with further increase in site-dilution. Finally, the system loses the magnetic order and the insulating state for $x=0.15$, significantly below the classical percolation threshold $x_p^{sc} (\sim 0.31$). We show that the induced moments on $U=0$ sites drive the magnetic order below the classical percolation limit by studying local moment systematics and finite-size analysis of magnetic order. At the end, we show that either increasing $U$ to large values or raising temperature beyond a $U$ dependent critical value, suppresses the induced local moments of the $U=0$ sites and recovers the classical percolation threshold.