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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.03149 |
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| _version_ | 1866917121018036224 |
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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 |