Accelerating Nonequilibrium Green functions simulations: the G1-G2 scheme and beyond
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866912993762082816 |
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| author | Bonitz, Michael Joost, Jan-Philip Makait, Christopher Schroedter, Erik Karsberger, Tim Balzer, Karsten |
| author_facet | Bonitz, Michael Joost, Jan-Philip Makait, Christopher Schroedter, Erik Karsberger, Tim Balzer, Karsten |
| contents | The theory of Nonequilibrium Green functions (NEGF) has seen a rapid development over the recent three decades. Applications include diverse correlated many-body systems in and out of equilibrium. Very good agreement with experiments and available exact theoretical results could be demonstrated if the proper selfenergy approximations were used. However, full two-time NEGF simulations are computationally costly, as they suffer from a cubic scaling of the computation time with the simulation duration. Recently we have introduced the G1-G2 scheme that exactly reformulates the Kadanoff-Baym ansatz with Hartree-Fock propagators (HF-GKBA) into time-local equations, allowing for a dramatic reduction of the scaling to time-linear scaling [Schluenzen et al., Phys. Rev. Lett. \textbf{124}, 076601 (2020)]. Remarkably, this scaling is achieved quickly, and also for high-level selfenergies, including the nonequilibrium $GW$ and $T$-matrix approximations [Joost et al., Phys. Rev. B \textbf{101}, 245101 (2020)]. Even the dynamically screened ladder approximation is now feasible [Joost et al., Phys. Rev. B \textbf{105}, 165155 (2022)], and also applications to electron-boson systems were demonstrated. Here we present an overview on recent results that were achieved with the G1--G2 scheme. We discuss problems and open questions and present further ideas how to overcome the current limitations of the scheme.We illustrate the G1--G2 scheme by presenting applying it to the excitation dynamics of Hubbard clusters, to optical excitation of graphene, and to charge transfer during stopping of ions by correlated materials. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_15030 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Accelerating Nonequilibrium Green functions simulations: the G1-G2 scheme and beyond Bonitz, Michael Joost, Jan-Philip Makait, Christopher Schroedter, Erik Karsberger, Tim Balzer, Karsten Strongly Correlated Electrons Plasma Physics The theory of Nonequilibrium Green functions (NEGF) has seen a rapid development over the recent three decades. Applications include diverse correlated many-body systems in and out of equilibrium. Very good agreement with experiments and available exact theoretical results could be demonstrated if the proper selfenergy approximations were used. However, full two-time NEGF simulations are computationally costly, as they suffer from a cubic scaling of the computation time with the simulation duration. Recently we have introduced the G1-G2 scheme that exactly reformulates the Kadanoff-Baym ansatz with Hartree-Fock propagators (HF-GKBA) into time-local equations, allowing for a dramatic reduction of the scaling to time-linear scaling [Schluenzen et al., Phys. Rev. Lett. \textbf{124}, 076601 (2020)]. Remarkably, this scaling is achieved quickly, and also for high-level selfenergies, including the nonequilibrium $GW$ and $T$-matrix approximations [Joost et al., Phys. Rev. B \textbf{101}, 245101 (2020)]. Even the dynamically screened ladder approximation is now feasible [Joost et al., Phys. Rev. B \textbf{105}, 165155 (2022)], and also applications to electron-boson systems were demonstrated. Here we present an overview on recent results that were achieved with the G1--G2 scheme. We discuss problems and open questions and present further ideas how to overcome the current limitations of the scheme.We illustrate the G1--G2 scheme by presenting applying it to the excitation dynamics of Hubbard clusters, to optical excitation of graphene, and to charge transfer during stopping of ions by correlated materials. |
| title | Accelerating Nonequilibrium Green functions simulations: the G1-G2 scheme and beyond |
| topic | Strongly Correlated Electrons Plasma Physics |
| url | https://arxiv.org/abs/2312.15030 |