Mathematical Physical Study of Ferromagnetism in Many-Electron Systems

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400407
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Gakushuin University
• Principal Investigator: Tasaki Hal 学習院大学, 理学部, 教授 (50207015)
• Co-Investigator(Kenkyū-buntansha): Tanaka Akinori 有明工業高等専門学校, 准教授 (80274512) ; Katsura Hosho 東京大学, 理学系研究科, 准教授 (80534594)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 数理物理 / 量子多体系 / 強相関電子系 / ハバード模型 / 金属強磁性 / マヨラナ端状態 / 朝永・ラッティンジャー液体

Outline of Final Research Achievements

The aim of the project had been to elucidate nontrivial orders and phase structures which emerge in strongly interacting many-body quantum systems, and, at the same time, to develop novel mathematical methods based on physical pictures and points of view. The most important achievement was a theorem which established the emergence of metallic ferromagnetism in the Hubbard type model which represents physically natural situation that "strong repulsion between electrons in a single band leads to ferromagnetic order". Notably a new mathematical method, especially suited for the study of metallic ferromagnetism, had been developed in this study. There was also progress in the researches of ferromagnetsim in a gapless multi-band Hubbard model, the emergence of Majorana edge states in some strongly interacting electron systems, and the Tomonoga-Luttinger liquid in the Bose-Hubbard models with flat-bands.

Free Research Field

統計物理学