Low-energy dynamics of the two-dimensional S=1/2 Heisenberg antiferromagnet on percolating clusters

TL;DR

This study explores the quantum dynamics of diluted two-dimensional S=1/2 Heisenberg antiferromagnetic clusters at the percolation threshold, revealing a dynamic exponent linked to the fractal nature of the clusters.

Contribution

It introduces a novel analysis of the low-energy excitations and dynamic scaling behavior of percolating antiferromagnetic clusters using combined numerical methods.

Findings

The dynamic exponent z is approximately equal to 2 times the fractal dimension D_f.

Low-energy excitations are caused by weakly coupled effective moments due to local sublattice imbalance.

Scaling of the gap distribution follows Delta ~ 1/L^z, with z related to fractal properties.

Abstract

We investigate the quantum dynamics of site diluted S=1/2 Heisenberg antiferromagnetic clusters at the percolation threshold. We use Lanczos diagonalization to calculate the lowest excitation gap Delta and, to reach larger sizes, study an upper bound for Delta obtained from sum rules involving the staggered structure factor and susceptibility, which we evaluate by quantum Monte Carlo simulations. Scaling the gap distribution with the cluster length L, Delta sim 1/L^z, we obtain a dynamic exponent z approximate 2D_f, where D_f=91/48 is the fractal dimensionality of the percolating cluster. This is in contrast to previous expectations of z=D_f. We argue that the low-energy excitations are due to weakly coupled effective moments formed due to local imbalance in sublattice occupation.