Excitations and Quantum Fluctuations in Site Diluted Two-Dimensional Antiferromagnets

TL;DR

This study investigates how site dilution and quantum fluctuations influence low-energy excitations and long-range order in two-dimensional antiferromagnets, revealing fracton-like excitations and a quantum fluctuation bound consistent with experiments.

Contribution

It provides a detailed analysis of quantum fluctuations and excitations in diluted 2D antiferromagnets, confirming the persistence of order up to the percolation threshold and identifying fracton-like excitations.

Findings

Long-range order persists up to the percolation threshold.

Fracton-like excitations appear at high frequencies.

Quantum fluctuations are bounded, preventing a quantum critical point below the threshold.

Abstract

We study the effect of site dilution and quantum fluctuations in an antiferromagnetic spin system on a square lattice within the linear spin-wave approximation. By performing numerical diagonalization in real space and finite-size scaling, we characterize the nature of the low-energy spin excitations for different dilution fractions up to the classical percolation threshold. We find nontrivial signatures of fractonlike excitations at high frequencies. Our simulations also confirm the existence of an upper bound for the amount of quantum fluctuations in the ground state of the system, leading to the persistence of long-range order up to the percolation threshold. This result is in agreement with recent neutron-scattering experimental data and quantum Monte Carlo numerical calculations. We also show that the absence of a quantum critical point below the classical percolation threshold holds for a large class of systems whose Hamiltonians can be mapped onto a system of coupled noninteracting massless bosons.