developing the modern theory for multipole moments in quantum many-body systems

2023 Fiscal Year Final Research Report

• Project/Area Number: 20H01825
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Review Section: Basic Section 13010:Mathematical physics and fundamental theory of condensed matter physics-related
• Research Institution: The University of Tokyo
• Principal Investigator: Watanabe Haruki 東京大学, 大学院工学系研究科(工学部), 准教授 (20785323)
• Project Period (FY): 2020-04-01 – 2024-03-31
• Keywords: 角電荷 / 四重極子 / 多極子 / 量子多体系 / トポロジカル秩序

Outline of Final Research Achievements

This research was aimed at generalizing the modern theory on the polarization and the orbital magnetization of insulators to higher order moments such as quadrupoles. In fact, several results were obtained for insulators with quadrupole and octupole moments, including their formulation and the prediction of fractional angular charges. Another direction obtained through these studies is that, in studying non-uniform symmetries, important findings on degeneracy of the ground states of topologically ordered phases and spontaneously symmetry-breaking phases were obtained in this study.

Free Research Field

物性理論

Academic Significance and Societal Importance of the Research Achievements

本研究を通して得られた角電荷についての一般的な公式は、NaClといった身近な結晶の角に現れる電荷を予言し、融解や反応性なども含めた物質の特性を理解する上でも重要な意味を持つと考えられる。またトポロジカル秩序や自発的対称性の破れを実現する状態でも系の大きさによっては基底状態の縮退をもたないという研究成果は量子多体系についての統一的な理解を目指す上で重要になると考えられる。