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Variety and universality of bulk-edge correspondence in topological phases: From solid state physics to transdisciplinary concepts
Grant-in-Aid for Scientific Research (S) Project No.17H06138
May 31, 2017 - March 31, 2022
♥ Public information



Project leader :
Y. Hatsugai (Univ. Tsukuba)
Core Member (alphabetical) :
H. Aoki (Univ. Tokyo)
T. Fukui (Ibaragi Univ.)
S. Iwamoto, (Univ. Tokyo )
T. Kawarabayashi (Toho Univ.)
A. Kimura (Hiroshima Univ.)
Y. Takahashi (Kyoto Univ.)
Adjunct Member (alphabetical):
M. Furuta (Univ. Tokyo)
 K. Imura, (Hiroshima Univ. )
T. Kariyado (NIMS)
S. Nakajima (Kyoto Univ.)
Project Researchers (appointed order)
Tomonari Mizoguchi (Assistant professor, Univ. of Tsukuba) : March 1, 2018-Dec.31, 2018 (Moved to tenure track assistant professor from Jan.1, 2019)
Hideaki Iwasawa (Program-specific associate professor, Hiroshima Univ.) : June.1, 2018-March31, 2020 (Move to National Institutes for QUantum and Eadiological Science and Technology from April 1, 2020))
Nobuyuki Takei (Program-specific associate professor, Kyoto Univ.) : Sep.1, 2018-March 31, 2020.
Yoshihito Kuno (Assistant professor, Univ. of Tsukuba) : March 1, 2020-

Related project
"Physics of bulk-edge correspondence and its universality in topological phases: From solid state physics to cold atoms" (FY2014-FY 2016)

♣ Meeting
1. Start-up Meeting
Univ. Tsukuba, Meyogadani, Bunkyo-ku, Tokyo, June 25 (2017)
2. International workshop : Variety and universality of bulk-edge correspondence 2018 (BEC2018), Jan.4-Jan.8 (2018)
73 registered participants.
3. 3rd Informal workshop, May 19-20 (2018)
Univ. Tsukuba, Tsukuba
4. International workshop : Variety and universality of bulk-edge correspondence 2018X (BEC2018X) , Dec.9-Dec.13 (2018)
Tokyo Campus, Univ. Tsukuba, Myogadani, Tokyo
5. NTTI2019 & BEC 2019 at Hiroshima, July 14-19 (2019): International workshop : Variety and universality of bulk-edge correspondence 2019 (BEC2019) jointed with "New Trends in Topological Insulators 2019 (NTTI2019)"
6. International workshop : Variety and universality of bulk-edge correspondence in topological phases:From solid state physics to transdisciplinary concepts" (BE/BC2020F, Bulk-Edge/Boundary Correspondence), Feb. 28-29 (2020)
Tokyo Campus, Univ. Tsukuba, Myogadani, Tokyo : Due to the Corona-virus outbreak in Japan, the real meeting is canceled and made "virtual".
7. 7-th Informal meeting with invited speakers, Oct. 20 (2020): zoom

BEC Seminar

♦ Job opening
1. Open position for assistant professor: Theory of topological phases (Univ. of Tsukuba) : Decided. Dr. Mizoguchi Tomonari. Thank you for the applications.
2. August 2019: Open position for assistant professor (Univ. of Tsukuba) : Decided. Dr. Yoshihito Kuno. Thank you for the applications.
General articles
1. Japansese only
2. Japansese only
3. Only in Japanese
4. Japanese only
5. Japanese only
6. Japanese only
7. Japanese only
8. Japanese only

★ For specialists
1. Bulk-edge correspondence
2. Japanese article

★ Focus lecture
Kyushu Univ. (supported by the present project)
Chiba Univ.(2015), Hiroshima Univ.2012) (before the project)

VI. Physics of bulk-edge correspondence and its universality in topological phases: From solid state physics to cold atoms (FInished) April 2014 - March 2017
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A HAPPY NEW YEAR 2020, -883 days left this year !
Recent News
Poster : hatsugai on 2020-11-03 10:00:50 (3479 reads)

Thouless' (adiabatic) pump in one-dimension 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 well-defined 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 bulk-edge 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 "Interaction-induced topological charge pump" by Yoshihito Kuno and Yasuhiro Hatsugai, Phys. Rev. Research 2, 042024(R), (2020) (Open access)

Poster : hatsugai on 2020-10-28 10:28:43 (4359 reads)

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.

Poster : hatsugai on 2020-10-01 16:07:56 (3774 reads)

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.

Poster : hatsugai on 2020-09-17 11:42:01 (3754 reads)

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).

Poster : hatsugai on 2020-08-16 14:53:28 (4012 reads)

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.

    Bulk-edge correspondence
    [0] バルクとエッジ
    [1] Focus lecture
    [2] Original papers
    [3] Japanese Physical Society monthly issue Commentary (Only Japanese except abstract) [pdf]
    [4] "Band gap, dangling bond and spin : a physicist's viewpoint" [pdf]
    Topological phases
    [0]Historical project
    KAKEN-HI DB FY1992 : Topological effects in electronic/spin systems
    KAKEN-HI DB FY1994 : Topology & geometrical phases in condensed matter physics
    Some of my talk files
    [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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