Dynamic mode decomposition for extrapolating nonequilibrium Green's-function dynamics
Abstract
The Hartree-Fock generalized Kadanoff-Baym ansatz (HF-GKBA) offers an approximate numerical procedure for propagating the two-time nonequilibrium Green's function (NEGF). Here, using the GW self-energy, we compare the HF-GKBA to exact results for a variety of systems with long- and short-range interactions, different two-body interaction strengths, and various nonequilibrium preparations. We find excellent agreement between the HF-GKBA and exact time evolution in models when more realistic long-range exponentially decaying interactions are considered. Furthermore, this agreement persists for long times and for intermediate to strong interaction strengths. In large systems, HF-GKBA becomes prohibitively expensive for long-time evolutions. For this reason, we look at the use of dynamical mode decomposition (DMD) to reconstruct long-time NEGF trajectories from a sample of the initial trajectory. Using no more than 16% of the total time evolution, we reconstruct the total trajectory with high fidelity. Our results show the potential for DMD to be used in conjunction with HF-GKBA to calculate long-time trajectories in large-scale systems.
- Authors:
-
- Univ. of California, Santa Barbara, CA (United States)
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Publication Date:
- Research Org.:
- Univ. of California, Santa Barbara, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC)
- OSTI Identifier:
- 1958168
- Grant/Contract Number:
- SC0022198
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 107; Journal Issue: 7; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Electronic structure; First-principles calculations; Approximation methods for many-body systems; GW method; Green's function methods; Many-body techniques
Citation Formats
Reeves, Cian C., Yin, Jia, Zhu, Yuanran, Ibrahim, Khaled Z., Yang, Chao, and Vlček, Vojtěch. Dynamic mode decomposition for extrapolating nonequilibrium Green's-function dynamics. United States: N. p., 2023.
Web. doi:10.1103/physrevb.107.075107.
Reeves, Cian C., Yin, Jia, Zhu, Yuanran, Ibrahim, Khaled Z., Yang, Chao, & Vlček, Vojtěch. Dynamic mode decomposition for extrapolating nonequilibrium Green's-function dynamics. United States. https://doi.org/10.1103/physrevb.107.075107
Reeves, Cian C., Yin, Jia, Zhu, Yuanran, Ibrahim, Khaled Z., Yang, Chao, and Vlček, Vojtěch. Fri .
"Dynamic mode decomposition for extrapolating nonequilibrium Green's-function dynamics". United States. https://doi.org/10.1103/physrevb.107.075107. https://www.osti.gov/servlets/purl/1958168.
@article{osti_1958168,
title = {Dynamic mode decomposition for extrapolating nonequilibrium Green's-function dynamics},
author = {Reeves, Cian C. and Yin, Jia and Zhu, Yuanran and Ibrahim, Khaled Z. and Yang, Chao and Vlček, Vojtěch},
abstractNote = {The Hartree-Fock generalized Kadanoff-Baym ansatz (HF-GKBA) offers an approximate numerical procedure for propagating the two-time nonequilibrium Green's function (NEGF). Here, using the GW self-energy, we compare the HF-GKBA to exact results for a variety of systems with long- and short-range interactions, different two-body interaction strengths, and various nonequilibrium preparations. We find excellent agreement between the HF-GKBA and exact time evolution in models when more realistic long-range exponentially decaying interactions are considered. Furthermore, this agreement persists for long times and for intermediate to strong interaction strengths. In large systems, HF-GKBA becomes prohibitively expensive for long-time evolutions. For this reason, we look at the use of dynamical mode decomposition (DMD) to reconstruct long-time NEGF trajectories from a sample of the initial trajectory. Using no more than 16% of the total time evolution, we reconstruct the total trajectory with high fidelity. Our results show the potential for DMD to be used in conjunction with HF-GKBA to calculate long-time trajectories in large-scale systems.},
doi = {10.1103/physrevb.107.075107},
journal = {Physical Review. B},
number = 7,
volume = 107,
place = {United States},
year = {Fri Feb 03 00:00:00 EST 2023},
month = {Fri Feb 03 00:00:00 EST 2023}
}
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FIG. 1: A) Model system with exponentially decaying interactions and an alternating local potential described by equations (1), (2) and (3). B) Outline of non-equilibrium preparation and DMD fitting procedure
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