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

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 (TN ). For the non-perturbative regime of U ∼ bandwidth, we find a rapid suppression of T * with reducing x from 1 to 0.7. However, TN remains unchanged in this dilution range, showing a weakening of the insulating state but not of the magnetic order. At x ≤ 0.7, T * and TN 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 sc p (∼ 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.

Itinerant ferromagnetism in a spin-fermion model for diluted spin systems

“…We reduce the quartic fermion problem present in repulsive Hubbard model into a quadratic one by introducing Hubbard-Stratonovich field and extract the following effective spin-fermion type Hamiltonian by suppressing the imaginary-time dependence from the Hubbard-Stratonovich fields (for details please see Refs. [ 45,46]). Then above Hamiltonian transfers to…”

“…x = 1 limit) at half filling using a semi-classical Monte Carlo (s-MC) approach 45 that matches well with DQMC results 47 . Recently, we have used s-MC approach to show that the antiferromagnetic order persists beyond the classical percolation threshold in the diluted one-band Hubbard model at absolute half filling in three dimensions 46 .…”