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初貝 安弘
筑波大学
理工学群副学群長
数理物質系物理学域
筑波大学大学院
数理物質科学研究科
物理学専攻 教授
学際物質科学研究センター(TIMS)教授
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[F]  2013 EMN West Meeting on Topological Insulators,  Houston, USA  Jan 7-10(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 co-dimenison 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 charge-flux 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.
前
[P] Seminar at M. Ueda Group, Univ. Tokyo, JAPAN, Jan 24 (2013)
カテゴリートップ
国際会議、研究会、セミナー
次
[P] Topological states of matter, Aspen, USA Jan 13--18 (2013)

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最新ニュース
投稿者 : hatsugai 投稿日時: 2017-12-26 01:33:43 (68 ヒット)

最近の研究成果トピックスとして2017年度の科研費ニュース vol.3 にトポロジカル相とバルク・エッジ対応の関係の解説を我々の研究の背景として書きました。予備知識は不要ですのでご興味のある方はご覧下さい。「トポロジカル物質におけるバルク・エッジ対応」


投稿者 : hatsugai 投稿日時: 2017-12-22 19:52:51 (48 ヒット)

Michel Fruchart (Instituut-Lorentz Universiteit, Leiden) will give a talk on Jan.9 (2018), 10:30 am at Rm. B602 by the title Topology of effective evolutions: oriented scattering networks and the phase rotation symmetry


投稿者 : hatsugai 投稿日時: 2017-12-22 11:33:02 (45 ヒット)

Christopher Mudry (Paul Scherrer Institute, Switzerland) gives a talk by the title "Abelian topological order in three-dimensional space" at Rm. B602 from 14:00 on Dec.28, (2017). The detail is here


投稿者 : hatsugai 投稿日時: 2017-11-27 18:03:29 (184 ヒット)

We are organizing an "International workshop : Variety and universality of bulk-edge correspondence 2018 (BEC2018) . Please do not confuse with Bose-Einstein condensation :) Its program is ready.


投稿者 : hatsugai 投稿日時: 2017-10-06 16:36:02 (133 ヒット)

The entanglement Chern numbers is a Chern number of an entanglement Hamiltonian which characterizes topological properties of a topological phase. Starting from a pure state density matrix of the ground state, one may obtain finite temperature (mixed state) density matrix by tracing out parts of the system. If the entanglement hamiltonian has a finite energy gap, the Chern number is well defined by lowering the temperature. We apply the concept for the 3D topological phases.The parity of the number of the Weyl point gives a well defined topological number to distinguish the the state is topologically non trivial. Have a look at arXiv 1708.03722 . The paper has been accepted for publication in Physical Review B.


    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」 [JPS-HP] [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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