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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29年の新年あけましておめでとうございます。今年もあと43日!
投稿者 : hatsugai 投稿日時: 2017-10-06 16:36:02 (77 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.

投稿者 : hatsugai 投稿日時: 2017-08-17 17:01:30 (300 ヒット)

初貝研究室では今回助教2名を公募いたします(公募締め切り2017年9月15日)。委細は [助教公募] をご確認ください。適任者のご推薦、ご応募の方よろしくお願いいたします。

投稿者 : hatsugai 投稿日時: 2017-08-17 17:00:09 (342 ヒット)

We are organizing a Japan-Swiss workshop TTCM2017 at EPOCHAL Tsukuba, Sep.10-13 (2017). Limited number of posters will be still accepted.

投稿者 : hatsugai 投稿日時: 2017-08-03 13:38:17 (263 ヒット)

A numerical scheme to calculate the many body Chern number for a ground state multiplet is formulated and explicitly given for projected bands of any lattice. We demonstrate its validity for lattice analogue of the nu=1/3 and 1/2 states. The string gauge to realize the minimum flux compatible with the periodicity of the unit cell is also presented. [arXiv:1707.06722]. The paper is published in JPSJ lett.

    [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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