Self-learning Monte Carlo method and cumulative update in fermion systems
Open accessAbstract
We develop the self-learning Monte Carlo (SLMC) method, a general-purpose numerical method recently introduced to simulate many-body systems, for studying interacting fermion systems. Our method uses a highly efficient update algorithm, which we design and dub ``cumulative update'', to generate new candidate configurations in the Markov chain based on a self-learned bosonic effective model. From a general analysis and a numerical study of the double exchange model as an example, we find that the SLMC with cumulative update drastically reduces the computational cost of the simulation, while remaining statistically exact. Remarkably, its computational complexity is far less than the conventional algorithm with local updates.
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ML offers a radically new approach that can potentially lead to discovery of new and more efficient algorithms.
“ML offers a radically new approach, which, in addition to the optimisation of existing algorithms (Shanahan, 2018), can potentially lead us towards the discovery of new and more efficient ones (Liu, 2017).”
From Artificial Intelligence (AI): Multidisciplinary perspectives on emerging challenges, opportunities, and agenda for research, practice and policy (2021) · cites this paper as Liu, 2017
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“ML o ff ers a radically new approach, which, in addition to the optimisation of existing algorithms (Shanahan, Trewartha, & Detmold, 2018), can potentially lead us towards the discovery of new and more e ffi cient ones (Liu, Qi, Yang Meng, and Fu, 2017).”
BackgroundExpressive power of parametrized quantum circuits
Du, Y., Hsieh, M.-H., Liu, T., & Tao, D. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.033125 · Cited by 318 · see citing works
- Authors
- Liu, J., Shen, H., Qi, Y., Meng, Z. Y., & Fu, L.
- Affiliations
- Massachusetts Institute of Technology (US)
- Chinese Academy of Sciences (CN)
- Venue
- Physical Review B
- Publisher
- American Physical Society (APS)
- Published
- 2017-06-07
- Volume
- 95
- Issue
- 24
- ISSN
- 2469-9950 (ISSN-L)
- 2469-9969
- OpenAlex
- W2557778781
- Cited by
- 82
- References
- 2
- Citations by year
- 2026: 2 · 2024: 2 · 2023: 8 · 2022: 8 · 2021: 9 · 2020: 16 · 2019: 14 · 2018: 15 · 2017: 8
- FWCI
- 8.67
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Physical review. B./Physical review. B (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- Rare & Special e-Zone (The Hong Kong University of Science and Technology) (submittedVersion)
- arXiv (Cornell University)
- Funders
- U.S. Department of Energy (DE-SC0010526, DE-SC0001299/DE-FG02-09ER46577)
- David and Lucile Packard Foundation
- Massachusetts Institute of Technology
- Ministry of Science and Technology of the People's Republic of China (2016YFA0300502)
- National Natural Science Foundation of China (11421092, 11574359)
- Topics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum many-body systems
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Physics of Superconductivity and Magnetism
- Keywords
- interacting fermions, double exchange model, Markov chains, computational complexity reduction, many-body simulation
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