Discrete Geometric Analysis for Quantum Spin System

2017 Fiscal Year Final Research Report

• Project/Area Number: 24244004
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Tohoku University
• Principal Investigator: Kotani Motoko 東北大学, 理学研究科, 教授 (50230024)
• Co-Investigator(Kenkyū-buntansha): 熊谷 隆 京都大学, 数理解析研究所, 教授 (90234509) ; 塩谷 隆 東北大学, 理学研究科, 教授 (90235507)
• Co-Investigator(Renkei-kenkyūsha): Obata Nobuaki 東北大学, 情報科学研究科, 教授 (10169360) ; Tate Tatsuya 東北大学, 理学研究科, 教授 (00317299) ; Miyaoka Reiko 東北大学, 高度教養教育, 学生支援機構, 総長特命教授 (70108182)
• Project Period (FY): 2012-04-01 – 2017-03-31
• Keywords: 幾何学 / 離散幾何学 / スペクトル解析 / スピン系

Outline of Final Research Achievements

We study mathematical framework for Quantum spin system. Physics on topological Insulator and topologically protected surface/edge state is formulated in K-theory. By using the non-commutative geometry, we generalized it to disordered systems. We also develop discrete surface theory to study the relation of microscopic structural data and macroscopic properties and apply it to carbon networks.

Free Research Field

幾何学、離散幾何解析学