A high-order regularized delta-Chebyshev method for computing spectral densities

TL;DR

This paper presents a high-order delta-Chebyshev method for efficiently computing spectral densities, notably the local density of states in complex materials like graphene, achieving rapid convergence with minimal additional computational cost.

Contribution

It introduces a novel high-order regularized delta-Chebyshev method that improves convergence in spectral density computations compared to existing kernel polynomial methods.

Findings

High-order convergence demonstrated on graphene models

Efficient computation with minimal extra cost

Applicable to smooth spectral densities in large systems

Abstract

We introduce a numerical method for computing spectral densities, and apply it to the evaluation of the local density of states (LDOS) of sparse Hamiltonians derived from tight-binding models. The approach, which we call the high-order delta-Chebyshev method, can be viewed as a variant of the popular regularized Chebyshev kernel polynomial method (KPM), but it uses a high-order accurate approximation of the $\delta$-function to achieve rapid convergence to the thermodynamic limit for smooth spectral densities. The costly computational steps are identical to those for KPM, with high-order accuracy achieved by an inexpensive post-processing procedure. We apply the algorithm to tight-binding models of graphene and twisted bilayer graphene, demonstrating high-order convergence to the LDOS at non-singular points.