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}
}
Figures / Tables:
Works referenced in this record:
Self-consistency in
G W Γ
formalism leading to quasiparticle-quasiparticle couplings
journal, October 2022
- Mejuto-Zaera, Carlos; Vlček, Vojtěch
- Physical Review B, Vol. 106, Issue 16
Dynamic mode decomposition of numerical and experimental data
journal, July 2010
- Schmid, Peter J.
- Journal of Fluid Mechanics, Vol. 656
Generalized Kadanoff-Baym ansatz for deriving quantum transport equations
journal, November 1986
- Lipavský, P.; Špička, V.; Velický, B.
- Physical Review B, Vol. 34, Issue 10
G1-G2 scheme: Dramatic acceleration of nonequilibrium Green functions simulations within the Hartree-Fock generalized Kadanoff-Baym ansatz
journal, June 2020
- Joost, Jan-Philip; Schlünzen, Niclas; Bonitz, Michael
- Physical Review B, Vol. 101, Issue 24
Hamiltonian Systems and Transformation in Hilbert Space
journal, May 1931
- Koopman, B. O.
- Proceedings of the National Academy of Sciences, Vol. 17, Issue 5
Time propagation of the Kadanoff–Baym equations for inhomogeneous systems
journal, June 2009
- Stan, Adrian; Dahlen, Nils Erik; van Leeuwen, Robert
- The Journal of Chemical Physics, Vol. 130, Issue 22
Real-Time
G W
: Toward an
Ab Initio
Description of the Ultrafast Carrier and Exciton Dynamics in Two-Dimensional Materials
journal, January 2022
- Perfetto, E.; Pavlyukh, Y.; Stefanucci, G.
- Physical Review Letters, Vol. 128, Issue 1
Many-body quantum electrodynamics networks: Non-equilibrium condensed matter physics with light
journal, October 2016
- Le Hur, Karyn; Henriet, Loïc; Petrescu, Alexandru
- Comptes Rendus Physique, Vol. 17, Issue 8
Stochastic GW Calculations for Molecules
journal, September 2017
- Vlček, Vojtěch; Rabani, Eran; Neuhauser, Daniel
- Journal of Chemical Theory and Computation, Vol. 13, Issue 10
Dynamic Mode Decomposition
book, January 2016
- Kutz, J. Nathan; Brunton, Steven L.; Brunton, Bingni W.
- Society for Industrial and Applied Mathematics
Hubbard nanoclusters far from equilibrium
journal, September 2014
- Hermanns, Sebastian; Schlünzen, Niclas; Bonitz, Michael
- Physical Review B, Vol. 90, Issue 12
The non-equilibrium Green function approach to inhomogeneous quantum many-body systems using the generalized Kadanoff–Baym ansatz
journal, November 2012
- Hermanns, S.; Balzer, K.; Bonitz, M.
- Physica Scripta, Vol. T151
Attosecond physics
journal, February 2009
- Krausz, Ferenc; Ivanov, Misha
- Reviews of Modern Physics, Vol. 81, Issue 1
Successes and Failures of Kadanoff-Baym Dynamics in Hubbard Nanoclusters
journal, October 2009
- von Friesen, M. Puig; Verdozzi, C.; Almbladh, C. -O.
- Physical Review Letters, Vol. 103, Issue 17
Dynamical Systems of Continuous Spectra
journal, March 1932
- Koopman, B. O.; Neumann, J. v.
- Proceedings of the National Academy of Sciences, Vol. 18, Issue 3
On dynamic mode decomposition: Theory and applications
journal, December 2014
- Kutz, J. Nathan; Brunton, Steven L.; Luchtenburg, Dirk M.
- Journal of Computational Dynamics, Vol. 1, Issue 2
Artificial damping in the Kadanoff-Baym dynamics of small Hubbard chains
journal, April 2010
- Friesen, M. Puig von; Verdozzi, C.; Almbladh, C-O
- Journal of Physics: Conference Series, Vol. 220
Ergodic Theory, Dynamic Mode Decomposition, and Computation of Spectral Properties of the Koopman Operator
journal, January 2017
- Arbabi, Hassan; Mezić, Igor
- SIAM Journal on Applied Dynamical Systems, Vol. 16, Issue 4
The GW Compendium: A Practical Guide to Theoretical Photoemission Spectroscopy
journal, July 2019
- Golze, Dorothea; Dvorak, Marc; Rinke, Patrick
- Frontiers in Chemistry, Vol. 7
Applications of the dynamic mode decomposition
journal, August 2010
- Schmid, P. J.; Li, L.; Juniper, M. P.
- Theoretical and Computational Fluid Dynamics, Vol. 25, Issue 1-4, p. 249-259
Time-linear scaling nonequilibrium Green's function method for real-time simulations of interacting electrons and bosons. II. Dynamics of polarons and doublons
journal, March 2022
- Pavlyukh, Y.; Perfetto, E.; Karlsson, Daniel
- Physical Review B, Vol. 105, Issue 12
Swift beyond 10,000 electrons using sparse stochastic compression
journal, August 2018
- Vlček, Vojtěch; Li, Wenfei; Baer, Roi
- Physical Review B, Vol. 98, Issue 7
Breaking the Theoretical Scaling Limit for Predicting Quasiparticle Energies: The Stochastic Approach
journal, August 2014
- Neuhauser, Daniel; Gao, Yi; Arntsen, Christopher
- Physical Review Letters, Vol. 113, Issue 7
Using dynamic mode decomposition to predict the dynamics of a two-time non-equilibrium Green’s function
journal, October 2022
- Yin, Jia; Chan, Yang-hao; Jornada, Felipe H. da
- Journal of Computational Science, Vol. 64
Dynamically screened ladder approximation: Simultaneous treatment of strong electronic correlations and dynamical screening out of equilibrium
journal, April 2022
- Joost, Jan-Philip; Schlünzen, Niclas; Ohldag, Hannes
- Physical Review B, Vol. 105, Issue 16
Nonequilibrium Many-Body Theory of Quantum Systems
book, March 2013
- Stefanucci, Gianluca; van Leeuwen, Robert
Figures / Tables found in this record: