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Main Authors: Yi, Jinjing, Massatt, Daniel, Horning, Andrew, Luskin, Mitchell, Pixley, J. H., Kaye, Jason
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2512.03149
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author Yi, Jinjing
Massatt, Daniel
Horning, Andrew
Luskin, Mitchell
Pixley, J. H.
Kaye, Jason
author_facet Yi, Jinjing
Massatt, Daniel
Horning, Andrew
Luskin, Mitchell
Pixley, J. H.
Kaye, Jason
contents 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 $δ$-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.
format Preprint
id arxiv_https___arxiv_org_abs_2512_03149
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A high-order regularized delta-Chebyshev method for computing spectral densities
Yi, Jinjing
Massatt, Daniel
Horning, Andrew
Luskin, Mitchell
Pixley, J. H.
Kaye, Jason
Computational Physics
Disordered Systems and Neural Networks
Strongly Correlated Electrons
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 $δ$-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.
title A high-order regularized delta-Chebyshev method for computing spectral densities
topic Computational Physics
Disordered Systems and Neural Networks
Strongly Correlated Electrons
url https://arxiv.org/abs/2512.03149