Fast and Accurate Scheme for Green Functions and Eigenvectors: Regulated Polynomial Expansion without Gibbs Oscillation

Abstract

An oscillation-free Fourier expansion is proposed and applied to the polynomial expansion of resolvent operator, as an alternative treatment for Gibbs phenomenon to the kernel polynomial method (KPM) by Voter et al. [Phys. Rev. B 53 (1996) 12733]. Adopting regulated Legendre polynomial as basis functions, the recurrence algorithm underlying the KPM is practically preserved, while it eliminates unphysical oscillations entirely. The resolution is uniform in the frequency domain, and improved without limitation by extending the truncation range of the expansion. The method can also be used to calculate the eigenvector with remarkably high precision. It is further extended to the time domain, being able to deal with the quantum evolution in the same algorithm. A numerical test was performed against a lattice dynamics of 19³ atoms, as well as of a computer generated Lennard–Jones glass of 1000 atoms. Not only it serves as a most efficient simulation scheme for a bulk, confirmed was also that the calculation converges to exact results within realistic computation time.