Scaling up the lattice dynamics of amorphous materials by orders of magnitude

TL;DR

This paper extends the Kernel Polynomial Method to efficiently compute vibrational properties of large amorphous materials, enabling simulations of systems with up to a million atoms, vastly surpassing previous computational limits.

Contribution

The authors develop a scalable KPM-based approach for lattice dynamics, allowing large-scale vibrational analysis of amorphous materials with complex chemistry.

Findings

KPM results converge to direct diagonalization for smaller systems.

The method scales linearly with system size, enabling million-atom simulations.

Efficient computation of vibrational density of states and eigenmodes.

Abstract

We generalise the non-affine theory of viscoelasticity for use with large, well-sampled systems of arbitrary chemical complexity. Having in mind predictions of mechanical and vibrational properties of amorphous systems with atomistic resolution, we propose an extension of the Kernel Polynomial Method (KPM) for the computation of the vibrational density of states (VDOS) and the eigenmodes, including the $\Gamma$-correlator of the affine force-field, which is a key ingredient of lattice-dynamic calculations of viscoelasticity. We show that the results converge well to the solution obtained by direct diagonalization (DD) of the Hessian (dynamical) matrix. As is well known, the DD approach has prohibitively high computational requirements for systems with $N=10^4$ atoms or larger. Instead, the KPM approach developed here allows one to scale up lattice dynamic calculations of real materials up to $10^6$ atoms, with a hugely more favorable (linear) scaling of computation time and memory consumption with $N$.