2022 Fiscal Year Final Research Report
Improvement of Tensor Network Method and its Application to Classical/Quantum Spin Systems
| Project/Area Number |
19H01809
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| 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 |
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Principal Investigator |
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| Project Period (FY) |
2019-04-01 – 2023-03-31
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| Keywords | 統計力学 / 計算物理学 / 量子スピン系 / テンソルネットワーク |
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| Outline of Final Research Achievements |
Based on a new representation by tensor networks, we have developed new numerical methods for quantum many-body problems such as spin systems. For example, the tensor network representation we discovered for the two-dimensional Kitaev model, which is standard in topological quantum state studies, turned out mathematically equivalent to the loop gas model, one of the standard classical models in statistical mechanics. This representation can be used in developing numerical methods, which was applied to obtain phase diagrams for problems derived from the Kitaev model. In particular, we have discovered many quantum phases in models corresponding to compounds such as alpha-RuCl3.
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| Free Research Field |
数物系科学
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| Academic Significance and Societal Importance of the Research Achievements |
スピン系は，その単純さにも関わらず，臨界現象やトポロジカル量子相など，多くの多体物理現象を示すため，現象の本質を理解する上で重要である．このため，スピン系の特徴を調べるための多くの数値計算手法がこれまでに考案されてきたが，扱える系の大きさや精度の点で不満足な点が多かった．これを克服するために本研究課題において我々はテンソルネットワーク表現に基づく量子統計力学研究のための新しい数値計算手法を開発し，いくつかの典型的な問題にたいして適用して成果を挙げた．とくに，テンソルネットワーク法の一般の情報処理への展開についても新しい展望が開けたことは社会的な展開にもつながる成果である．
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