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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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ニュース!! : Generic construction of flat bands 投稿者 : hatsugai 投稿日時： 20190930 11:19:28 ( 1476 ヒット) Exact flatness of energy bands implies some reasons behind. Here we present one of them, "molecular orbital (MO) representation", which seems to be applied for various classes of tight binding models. Mathematically if the rank of the hamiltonian as a linear operator is less than the number of atomic sites, the kernel of the linear operator has a finite dimension. This is the zero mode flat band. The MO rep. presents nice physical reasons for it. Original proposal by YH with Isao Maruyama in 2011 in EPL and arXiv is counting dimensions of nonorthogonal projections but the hopping of the MO's is allowed as we pointed out (it should be). It's a fun to guess what kinds of the MO representation is possible for a known flat band system. Try !
Also several physical reason why the flat band crosses/touches to dispersive bands in many cases are discussed. Our new paper has appeared in EPL, "Molecularorbital representation of generic flatband models", by T. Mizoguchi and Y. Hatsugai , also arXiv. 投稿された内容の著作権はコメントの投稿者に帰属します。

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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25日！
最新ニュース
投稿者 : hatsugai 投稿日時： 20201103 10:00:50 ( 225 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 ( 479 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 ( 524 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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