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Web 記事 - トポロジカル秩序

トポロジカル秩序

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研究解説:  » 量子液体
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hatsugai 2009-11-25 18:18

近年の物性科学の進歩により、必ずしも対称性の破れを伴わないが極めて特徴的な物質相が存在することが明らかとなりました。歴史的にみて、その典 型例が量子ホール効果における種々の物質相です。2次元的に閉じこめられたお互いに斥力相互作用しあう電子群が磁場下に置かれたとき電子密度および磁場の 強度をいろいろと変化させると驚くほど多様な物質相が現れることが知られるに至りました。ところがその多くの物質相の間で古来用いられてきた局所的な秩序 変数により記述されるような対称性の違い、区別はその多くの場合全くなく、対称性的には同一の物質相として考えざるをえないのですが、明らかに一連の物質 相の性質は特徴的に異なり同一とはどうしてもいいがたいのです。そこで考えられたのがトポロジカル秩序といわれる新しい概念です。
トポロジカル 秩序とは局所秩序変数が局所場の場の理論にその起源をもつのに対応してWittenによるトポロジカルな場の理論において使われたいくつかの概念との類似 性を元にMITのX.-G.Wenにより初期の提案がなされたものです。たとえば、状態の縮退度が物理系の大域的な構造どのように依存するか等を相の特定 に使おうというわけです。近年私はよい広く、量子系固有の幾何学的位相を用いてトポロジカル秩序の概念を拡張し有効に利用する具体的手法を提案しいくつか の具体的試みを行っています。
振り返ってこの20年来の物性物理を考えるといくつもの新規な物質相が発見されてきましたが、真に興味深いのは、いわば未だによくわからない量子液体相であると考えられます。これら量子液体相においてこそ、幾何学的位相をもちいて拡張された新しい秩序概念としてのトポ ロジカル秩序が極めて有用なものとなると考えられるのです。これについては節を変えてまたご説明したいと思います。

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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63日!
最新ニュース
投稿者 : hatsugai 投稿日時: 2020-10-28 10:28:43 (152 ヒット)

The Dirac cone is a typical singular energy dispersion in two dimensions that is a source of various non-trivial topological effects. When realized in real/synthetic materials, it is generically tilted and the equi-energy surface (curve) can be elliptic/hyperbolic (type I/II). The type III Dirac cone is a critical situation between the type I and II that potentially causes various non-trivial physics. As for realization of the type III Dirac cones, we are proposing a generic theoretical scheme without any fine tuning of material parameters . It may also help to synthesize in meta materials. The molecular orbital (MO) construction of the generic flat bands which we are also proposing plays a crutial role. Have a look at "Type-III Dirac Cones from Degenerate Directionally Flat Bands: Viewpoint from Molecular-Orbital Representation" by Tomonari Mizoguchi and Yasuhiro Hatsugai, J. Phys. Soc. Jpn. 89, 103704 (2020) Also arXiv:2007.14643. The paper has been selected as an Editors' choice of J. Phys. Soc. Jpn. (Sep. 2020). See also "News and comments" by Prof. N. Nagaosa.


投稿者 : hatsugai 投稿日時: 2020-10-01 16:07:56 (189 ヒット)

Motivated by a historical example, the Dirac Hamiltonian as a square-root of the Klein-Gordon 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 “square-root higher order topological insulator (square-root 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, "Square-root higher-order 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: 2020-09-17 11:42:01 (105 ヒット)

As for a topological characterization of a full Liouvillian (including jump term) for the non hermitian fractional quantum Hall states, we are proposing a pseudospin Chern number associated with the Niu-Thouless-Wu type twists in the doubled Hilbert space. Numerical demonstration of the proposal is explicitely given and its validity is discussed. Have a look at "Fate of fractional quantum Hall states in open quantum systems: Characterization of correlated topological states for the full Liouvillian" by Tsuneya Yoshida, Koji Kudo, Hosho Katsura, and Yasuhiro Hatsugai, Phys. Rev. Research 2, 033428 (2020) (open access).


投稿者 : hatsugai 投稿日時: 2020-08-16 14:53:28 (266 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 well-established 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.


投稿者 : hatsugai 投稿日時: 2020-07-30 12:47:16 (252 ヒット)

Our article on non-hermitian band touching for strongly correlated systems has been published in PTEP (Progress of Theoretical and Experimental Physics), "Exceptional band touching for strongly correlated systems in equilibrium", by Tsuneya Yoshida, Robert Peters, Norio Kawakami, Yasuhiro Hatsugai. Focusing on the non-hermitian topological phenomena for the equilibrium Green function of correlated electrons, a compact review of the exceptonal band touching that is intrinsic for non-hermitian matrices is described as well. 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」 [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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