Site dilution of quantum spins in the honeycomb lattice

TL;DR

This paper investigates how site dilution affects the magnetic properties and density of states in quantum spins on a honeycomb lattice, using various theoretical and computational methods, and compares results with experimental data.

Contribution

It provides a detailed analysis of site dilution effects on quantum spins in the honeycomb lattice, including new Monte Carlo results and insights into the absence of quantum criticality.

Findings

Staggered magnetization of the undiluted system is approximately 0.2677.

Finite staggered magnetization persists at the percolation threshold, indicating no quantum critical transition.

Results align quantitatively with experimental measurements on specific honeycomb materials.

Abstract

We discuss the effect of site dilution on both the magnetization and the density of states of quantum spins in the honeycomb lattice, described by the antiferromagnetic Heisenberg spin-S model. For this purpose a real-space Bogoliubov-Valatin transformation is used. In this work we show that for the S>1/2 the system can be analyzed in terms of linear spin wave theory. For spin S=1/2, however, the linear spin wave approximation breaks down. In this case, we have studied the effect of dilution on the staggered magnetization using the Stochastic Series Expansion Monte Carlo method. Two main results are to be stressed from the Monte Carlo method: (i) a better value for the staggered magnetization of the undiluted system, m=0.2677(6); (ii) a finite value of the staggered magnetization of the percolating cluster at the classical percolation threshold, showing that there is no quantum critical transition driven by dilution in the Heisenberg model. In the solution of the problem using linear the spin wave method we pay special attention to the presence of zero energy modes. Using a combination of linear spin wave analysis and the recursion method we were able to obtain the thermodynamic limit behavior of the density of states for both the square and the honeycomb lattices. We have used both the staggered magnetization and the density of states to analyze neutron scattering experiments and Neel temperature measurements on quasi-two- -dimensional honeycomb systems. Our results are in quantitative agreement with experimental results on Mn_pZn_{1-p}PS_3 and on the Ba(Ni_pMg_{1-p})_2V_2O_8.