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ResercherID: Y. Hatsugai

[F]   MANA seminar & lectures at Prof. X. Hu Group at NIMS, Tsukuba, JAPAN, March 6 (2013)


MANA Seminar:
Title: "Topological phases and bulk-edge correspondence"
Quantum/spin liquids are states without any fundamental symmetry
breaking. They are featureless as a bulk but some of them possess
characteristic boundary states with edges or impurities.  Historical
and typical examples are quantum Hall states and Haldane spin chain.
Quantum spin Hall states as the topological insulators also belong to
it. Many of them are topologically nontrivial and it implies the
existence of edges states and vice versa. This is the bulk-edge
correspondence, which is further applied for variety of quantum states
such as graphene, anisotropic-superconductors, cold atoms and
photonics crystals. We will explain idea of topological phases and the
bulk-edge correspondence supplemented with examples.

"Characterization of topological phases"

1. Topological phases
1.1 Symmetry breaking and Nambu Goldstone boson
1.2 Quantum/Spin liquids
1.3 Quantum Hall states and adiabatic heuristic argument
1.4 Gapped or gapless

2. Topological order parameters
 2.1 Gap nodes
 2.2 Adiabatic invariants
 2.3 Bulk-edge correspondence
 2.4 Entanglement entropy

3. Berry connections
3.1 Chern numbers for the quantum Hall states
3.2 Berry phase and its quantization
3.3 Singlet/Dimer order parameter

4. Characterization for the zoo
 4.1 Quantum spin chains and ladders
 4.2 BEC-BCS crossover
 4.3 Orthogonal dimers
 4.4 Frustrated fermions

5. Bulk-edge correspondence
 5.1 QHE and zero modes of graphene
 5.2 Topological invariant of the edge states
 5.3 Exact bulk-edge correspondence
 5.3 Bulk-edge correspondence of Dirac fermions



[P]"Quantum effects in graphene and related material ", Univ. Tsukuba, Tsukuba, March 19 (2013)
[P] Seminar at M. Ueda Group, Univ. Tokyo, JAPAN, Jan 24 (2013)

今年もやります。まずは量子力学3. 冬は 統計力学2. 平成30年の新年あけましておめでとうございます。今年もあと289日!
投稿者 : hatsugai 投稿日時: 2017-12-26 01:33:43 (220 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 (203 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 (195 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 (460 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 (260 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.

    [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]
    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
    [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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