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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2405.06716 |
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| _version_ | 1866908284584198144 |
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| author | Kiese, Dominik Strand, Hugo U. R. Chen, Kun Wentzell, Nils Parcollet, Olivier Kaye, Jason |
| author_facet | Kiese, Dominik Strand, Hugo U. R. Chen, Kun Wentzell, Nils Parcollet, Olivier Kaye, Jason |
| contents | We present a generalization of the discrete Lehmann representation (DLR) to three-point correlation and vertex functions in imaginary time and Matsubara frequency. The representation takes the form of a linear combination of judiciously chosen exponentials in imaginary time, and products of simple poles in Matsubara frequency, which are universal for a given temperature and energy cutoff. We present a systematic algorithm to generate compact sampling grids, from which the coefficients of such an expansion can be obtained by solving a linear system. We show that the explicit form of the representation can be used to evaluate diagrammatic expressions involving infinite Matsubara sums, such as polarization functions or self-energies, with controllable, high-order accuracy. This collection of techniques establishes a framework through which methods involving three-point objects can be implemented robustly, with a substantially reduced computational cost and memory footprint. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06716 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Discrete Lehmann representation of three-point functions Kiese, Dominik Strand, Hugo U. R. Chen, Kun Wentzell, Nils Parcollet, Olivier Kaye, Jason Computational Physics Strongly Correlated Electrons Numerical Analysis We present a generalization of the discrete Lehmann representation (DLR) to three-point correlation and vertex functions in imaginary time and Matsubara frequency. The representation takes the form of a linear combination of judiciously chosen exponentials in imaginary time, and products of simple poles in Matsubara frequency, which are universal for a given temperature and energy cutoff. We present a systematic algorithm to generate compact sampling grids, from which the coefficients of such an expansion can be obtained by solving a linear system. We show that the explicit form of the representation can be used to evaluate diagrammatic expressions involving infinite Matsubara sums, such as polarization functions or self-energies, with controllable, high-order accuracy. This collection of techniques establishes a framework through which methods involving three-point objects can be implemented robustly, with a substantially reduced computational cost and memory footprint. |
| title | Discrete Lehmann representation of three-point functions |
| topic | Computational Physics Strongly Correlated Electrons Numerical Analysis |
| url | https://arxiv.org/abs/2405.06716 |