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初貝 安弘 筑波大学筑波大学大学院 数理物質科学研究科 物理学専攻 教授 初貝写真
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 [F] 2013 EMN West Meeting on Topological Insulators, Houston, USA Jan 710(2013) [ Web ]
 Invited: "Symmetry protection in topological phases"
 Yasuhiro Hatsugai
 Abstract
 One of the characteristic features of topological phases such as topological insulators is absence of the fundamental symmetry breaking which has been a basic concept in the description of conventional order. Still symmetry plays a central role for the topological phases as symmetry protection in several ways. Gapless node structure of anisotropic superconductors is topologically protected, which is a historical example [1,2]. Generically the symmetry governs the gapless phases with massless Dirac fermions in 2D, 3D and more [3,4] where the codimenison of the generic degeneracy is crucial. For the gapped phases, the symmetry again controls properties of the topological systems. In addition to the intrinsically quantized quantities such as the Chern numbers, one further has adiabatic invariants by symmetry protected quantization as the Z2 Berry phases and its generalization [4,5,6]. They are used as the topological order parameters. Specifically for the topological insulators, the time reversal symmetry (TR) and the associated Kramers (KR) degeneracy are fundamentally important. Then the natural tool for the description is a quaternion and the quaternionic Berry connections of the KR pair. Topological quantities with/without TR symmetry are described in a parallel way for the Chern numbers and symmetry protected quantized quantities [5]. Also the chargeflux duality of some 3D topological insulator on a frustrated lattice will be discussed [7].
 1. E. I. Blount, Phys. Rev. B 32, 2935 (1985).
2. G. E. Volovik, JETP Lett. 66, 522 (1997).
3. M. Creutz, JHEP 04, 017 (2008).
4. Y. Hatsugai, J. Phys. Soc. Japan 75, 123601 (2006).
5. Y. Hatsugai, New J. Phys. 12, 065004 (2010).
6. Y. Hatsugai and I. Maruyama, EPL 95, 20003 (2011).
7. Y. Hatsugai and Y. Avishai, to be published.
[P] Seminar at M. Ueda Group, Univ. Tokyo, JAPAN, Jan 24 (2013)

国際会議、研究会、セミナー

[P] Topological states of matter, Aspen, USA Jan 1318 (2013)


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現在の時刻
今年もやります。まずは 量子力学3（遠隔）.
冬は
統計力学2 改め物性理論ＩＩ (大学院「ベリー接続の理論とバルクエッジ対応」).
令和二年の新年あけましておめでとうございます。今年もあと342日！
最新ニュース
投稿者 : hatsugai 投稿日時： 20201103 10:00:50 ( 972 ヒット) Thouless' (adiabatic) pump in onedimension is a typical topological phenomena characterized by the Chern number that correspondes to the quantized motion of the center of mass (COM). Although the COM is only welldefined with boudary (to set the origin of the coordinate), the COM experimentally observed is given by the bulk and the edge states do not contribute. Ultimate adiabaticity, that has never been achieved experimentaly, supports the quantization of the COM supplemented by the periodicity of the system with boundaries. This is the unique bulkedge correspondence of the pump. We here propose a generic construction using a phase boundary line of the symmetry protect phase with two parameters works as a topological obstruction of the pump in extended parameter space. The construction is purely of manybody and the interaction can be one of the parameters. Have a look at "Interactioninduced topological charge pump" by Yoshihito Kuno and Yasuhiro Hatsugai, Phys. Rev. Research 2, 042024(R), (2020) (Open access) 投稿者 : hatsugai 投稿日時： 20201001 16:07:56 ( 1253 ヒット) Motivated by a historical example, the Dirac Hamiltonian as a squareroot of the KleinGordon Hamiltonian, its lattice analogue has been discussed recently. Zero energy states are shared by the parent and its descendant. The story is more than that. Not necessarily zero energy but its high energy part can also share topological characters. We hereby propose a “squareroot higher order topological insulator (squareroot HOTI)” when its squared parent is HOTI. Based on the simple observation that square of the decorated honeycomb lattice is given by a decoupled sum of the Kagome and honeycomb lattices, we have demonstrate that the “corner states” of the breezing Kagome lattice with boundaries share topological characters with its descendant as the decorated honeycomb lattice. Have a look at our recent paper just published online, "Squareroot higherorder topological insulator on a decorated honeycomb lattice" by Tomonari Mizoguchi, Yoshihito Kuno, and Yasuhiro Hatsugai, Phys. Rev. A 102, 033527 (2020), also arXiv:2004.03235. 投稿者 : hatsugai 投稿日時： 20200816 14:53:28 ( 1414 ヒット) Adiabatic deformation of gapped systems is a conceptual basis of topological phases. It implies that topological invariants of the bulk described by the Berry connection work as topological order parameters of the phase. This is independent of the wellestablished symmetry breaking scenario of the phase characterization. Adiabatic heuristic argument for the fractional quantum Hall states is one of the oldest such trials that states the "FRACTIONAL" state is deformed to the “INTEGER”. Although it is intuitive and physically quite natural, there exist several difficulties. How the states with different degeneracy are deformed each other adiabatically? We have clarified the questions and demonstrated this adiabatic deformation on a torus in the paper "Adiabatic heuristic principle on a torus and generalized Streda formula" by Koji Kudo and Yasuhiro Hatsugai , Phys. Rev. B 102, 125108 (2020) (also arXiv:2004.00859) What is deformed continuously is a gap not the states ! This is also sufficient for the topological stability of the Chern number (of the degenerate multiplet) as a topological order parameter. Have a look at. 検索
バルク・エッジ対応
 [0] バルクとエッジ
 [1] 集中講義
 [2] 原論文と解説
 [3] トポロジカル秩序とベリー接続：日本物理学会誌 「解説」 [JPSHP] [pdf]
 [4] "Band gap, dangling bond and spin : a physicist's viewpoint" [pdf] [Web]
トポロジカル相
[0]昔の科研費  科研費 1992年度：電子系スピン系におけるトポロジカル効果
 科研費 1994年度：物性論におけるトポロジーと幾何学的位相
私の講演ファイルのいくつか [1] MIT, Boston (2003)
 [2] APS/JPS March Meeting (2004)
 [3] JPS Fall meeting, JAPAN (2004)
 [4] APS/JPS March meeting (2005)
 [5] JPS Fall meeting (2005):Entanglement
 [6] Superclean workshop, Nasu (2006)
 [7] MPIPKS, Dresden (2006)
 [8] KEK, Tsukuba (2007)
 [9] ETH, Zurich (2008)
 [10] ICREA, Sant Benet (2009)
 [11] JPS Meeting, Kumamoto (2009)
 [12]HMF19, Fukuoka (2010)
 [13] NTU, Singapore (2011)
 [14] ICTP, Trieste (2011)
 [15] Villa conf., Orland (2012)
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