Fast Fourier-Chebyshev approach to real-space simulations of the Kubo formula
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866914684313010176 |
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| author | de Castro, Santiago Giménez Lopes, João M. Viana Parente Ferreira, Aires Bahamon, D. A. |
| author_facet | de Castro, Santiago Giménez Lopes, João M. Viana Parente Ferreira, Aires Bahamon, D. A. |
| contents | The Kubo formula is a cornerstone in our understanding of near-equilibrium transport phenomena. While conceptually elegant, the application of Kubo's linear-response theory to interesting problems is hindered by the need for algorithms that are accurate and scalable to large lattice sizes beyond one spatial dimension. Here, we propose a general framework to numerically study large systems, which combines the spectral accuracy of Chebyshev expansions with the efficiency of divide-and-conquer methods. We use the hybrid algorithm to calculate the two-terminal conductance and the bulk conductivity tensor of 2D lattice models with over $10^7$ sites. By efficiently sampling the microscopic information contained in billions of Chebyshev moments, the algorithm is able to accurately resolve the linear-response properties of complex systems in the presence of quenched disorder. Our results lay the groundwork for future studies of transport phenomena in previously inaccessible regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_09690 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fast Fourier-Chebyshev approach to real-space simulations of the Kubo formula de Castro, Santiago Giménez Lopes, João M. Viana Parente Ferreira, Aires Bahamon, D. A. Mesoscale and Nanoscale Physics The Kubo formula is a cornerstone in our understanding of near-equilibrium transport phenomena. While conceptually elegant, the application of Kubo's linear-response theory to interesting problems is hindered by the need for algorithms that are accurate and scalable to large lattice sizes beyond one spatial dimension. Here, we propose a general framework to numerically study large systems, which combines the spectral accuracy of Chebyshev expansions with the efficiency of divide-and-conquer methods. We use the hybrid algorithm to calculate the two-terminal conductance and the bulk conductivity tensor of 2D lattice models with over $10^7$ sites. By efficiently sampling the microscopic information contained in billions of Chebyshev moments, the algorithm is able to accurately resolve the linear-response properties of complex systems in the presence of quenched disorder. Our results lay the groundwork for future studies of transport phenomena in previously inaccessible regimes. |
| title | Fast Fourier-Chebyshev approach to real-space simulations of the Kubo formula |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2307.09690 |