Stabilizing the calculation of the self-energy in dynamical mean-field theory using constrained residual minimization
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866913758222221312 |
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| author | LaBollita, Harrison Kaye, Jason Hampel, Alexander |
| author_facet | LaBollita, Harrison Kaye, Jason Hampel, Alexander |
| contents | We propose a simple and efficient method to calculate the electronic self-energy in dynamical mean-field theory (DMFT), addressing a numerical instability often encountered when solving the Dyson equation. Our approach formulates the Dyson equation as a constrained optimization problem with a simple quadratic objective. The constraints on the self-energy are obtained via direct measurement of the leading order terms of its asymptotic expansion within a continuous time quantum Monte Carlo framework, and the use of the compact discrete Lehmann representation of the self-energy yields an optimization problem in a modest number of unknowns. We benchmark our method for the non-interacting Bethe lattice, as well as DMFT calculations for both model systems and ab-initio applications. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_01266 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Stabilizing the calculation of the self-energy in dynamical mean-field theory using constrained residual minimization LaBollita, Harrison Kaye, Jason Hampel, Alexander Strongly Correlated Electrons We propose a simple and efficient method to calculate the electronic self-energy in dynamical mean-field theory (DMFT), addressing a numerical instability often encountered when solving the Dyson equation. Our approach formulates the Dyson equation as a constrained optimization problem with a simple quadratic objective. The constraints on the self-energy are obtained via direct measurement of the leading order terms of its asymptotic expansion within a continuous time quantum Monte Carlo framework, and the use of the compact discrete Lehmann representation of the self-energy yields an optimization problem in a modest number of unknowns. We benchmark our method for the non-interacting Bethe lattice, as well as DMFT calculations for both model systems and ab-initio applications. |
| title | Stabilizing the calculation of the self-energy in dynamical mean-field theory using constrained residual minimization |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2310.01266 |