2023 Fiscal Year Final Research Report
Development of an analytic continuation method with guaranteed accuracy using information theory
Project/Area Number |
19K03649
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Review Section |
Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
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Research Institution | The University of Tokyo |
Principal Investigator |
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Co-Investigator(Kenkyū-buntansha) |
本山 裕一 東京大学, 物性研究所, 技術専門職員 (30816731)
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Project Period (FY) |
2019-04-01 – 2024-03-31
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Keywords | 解析接続 / スパースモデリング / 交差検証 / 虚時間グリーン関数 |
Outline of Final Research Achievements |
Quantum Monte Carlo methods are a powerful tool for making detailed comparisons with experimental data on static physical properties such as magnetization and specific heat. However, for dynamic physical quantities like spectral analysis of electronic states, there is no deterministic method for high-precision analytic continuation, making detailed comparisons with experiments difficult. This research aims to enhance the accuracy and reliability of analytic continuation, and to establish a technical foundation for precision-guaranteed comparisons between theoretical calculations and experimental results. To this end, we have implemented the verification of automatic hyperparameter estimation using cross-validation and developed analytic continuation methods for multi-orbital systems. Additionally, we have carried out the development and maintenance of related software to facilitate the design of functional materials.
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Free Research Field |
物性理論
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Academic Significance and Societal Importance of the Research Achievements |
本研究は、精度保証された高精度な解析接続を実現し、複雑なスペクトル構造や動的感受率を高精度に求めることを目的とする。これにより、現実物質を対象とした理論解析の基盤技術が構築される。本研究では、誤差増幅を抑制する計算手法の確立と、解析接続データの精度評価手法の確立を目指した。これにより、解析結果の定量的・客観的な精度評価が可能となり、解析の信頼度向上と計算コストの軽減が実現する。得られた高精度データはベーテ・サルピータ方程式などの応用計算に活用されることが期待され、理論解析の信頼性が向上し、幅広い材料科学分野への応用が期待される。
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