Geometrical and Algebraic Aspects of Condensed Matter Physics

凝聚态物理的几何和代数方面

• 批准号: 15540364
• 负责人: HATSUGAI Yasuhiro
• 金额: $ 2.24万
• 依托单位: the University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540364/
• 关键词: Topological Order; Anisotropic Superconductivity; Carbon 2D systems; Edge States; Quantum Liquids; Topological Invariants; Quantum Hall Effects; Quantum Entanglements; 幾何学的位相; カーボンナノチューブ; 局所磁気秩序; 時間反転対称性の破れ; ベリー接続; 非可換チャーン数; カーボン; 量子力学; 相分

It has been recognized that some of physically important quantum states are not well characterized by conventional order parameters. In such cases, geometrical phases which are characteristic in quantum physics play an important role. We try to characterize the states by the word "topological orders". Some of such states are polyacetylenes, quantum Hall states, two dimensional Carbon sheets, anisotropic superconductors with time reversal symmetry breaking and so on. In most cases, the topological orders are hidden in the bulk and reveal their characters near boundaries or defects as generalized edge states. Some of low dimensional quantum liquids can be also in the classes where topological invariants based on the Berry's connection may replace the conventional order parameters.

人们已经认识到，某些物理上重要的量子状态并未以常规顺序参数为特征。在这种情况下，在量子物理学中具有特征的几何阶段起着重要作用。我们试图通过“拓扑顺序”一词来表征状态。其中一些状态是聚乙酰基烯，量子霍尔状态，二维碳片，各向异性超导体，随时间逆转对称性破裂等。在大多数情况下，拓扑命令隐藏在批量上，并以广义边缘状态揭示其角色附近或缺陷。某些低维量子液体也可以在基于浆果连接的拓扑不变的类别中，可以替代常规订单参数。

项目成果

Magnetism in the 2D t-t' Hubbard model : from low to over doping

二维 t-t Hubbard 模型中的磁性：从低掺杂到过度掺杂

• 发表时间: 2005
• 期刊: Phys. Rev. B. 71
• 作者: H.Taniguchi;Y.Morita;Y.Hatsugai
• 通讯作者: Y.Hatsugai

Characterization of Topological insulator

拓扑绝缘体的表征

• 发表时间: 2005
• 期刊: J. Phy. Soc. Jpn. (Lett.) 74
• 作者: H.Taniguchi;Y.Morita;Y.Hatsugai;Y.Hatsugai
• 通讯作者: Y.Hatsugai

S.Ryu, Y.Hatsugai: "Zero energy edge states and chiral symmetry brealing at edges of graphite sheet"Physica E. (出版予定). (2004)

S.Ryu，Y.Hatsugai：“石墨片边缘的零能量边缘态和手性对称性破坏”Physica E.（即将出版）。

Zero energy edge states and chiral symmetry breaking at edges of graphite sheets

石墨片边缘的零能边缘态和手性对称性破缺

• 发表时间: 2004
• 期刊: Physica E 22
• 作者: S.Ryu;Y.Hatsugai
• 通讯作者: Y.Hatsugai

Y.Morita, S.Ryu, Y.Hatsugai: "Recent research develompmet in Physics, 4 "Emergence off(2+1)-dim. Dirac Fermion in condensed Matter""Transworld Reserch Network, India. 463-483(20) (2003)

Y.Morita、S.Ryu、Y.Hatsugai：“物理学的最新研究进展，4”Emergence off(2 1)-dim。