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HATSUGAI   Lab.     Institute of Physics, University of Tsukuba


L: Topological stability of Dirac cones, merging & C: fractal in graphene (Flying Butterfly) & R: Non Abelian gauge structure in solids
Refereneces :
[1] Y. Hatsugai, T. Fukui, H. Aoki, Phys. Rev. B 74, 205414 (2006) : [Journal Link] , arXiv:cond-mat/0607669
"Topological analysis of the quantum Hall effect in graphene"
[2] Y. Hatsugai, J. Phys. Soc. Jpn. 73, 2604 (2004) : [Journal Link] , arXiv:cond-mat/0405551
"Explicit Gauge Fixing for Degenerate Multiplets: A Generic Setup for Topological Orders"

Hatsugai Group, Condensed Matter Theory

Targets of our research is to explore new insight and find novel physical principles in condensed matter materials and phenomena. We have been working on the following topics. [paper]

[1] Geometrical phases of condensed matter physics
Target material and phenomena
(1) Graphene as a relativistic Dirac particle in solid states
(2) Quantum Hall effects as typical topological insulators
(3) Quantum spin Hall phase as a time reversal invariant topological insulator
(4) Electrons with strong correlation as non trivial quantum liquids
(5) Exotic superconductivity with anisotropic pairing
(6) Frustrated magnets as typical spin liquids
(7) Semiconductor nano-structures as a playground of novel quantum phenomena
(8) Universal edge states in quantum (spin) Hall effects, Haldane magnets, photonic crystals and cold atoms
(9) Aharonov-Bohm effect and its generalization

Theoretical methods and concepts
(1) Non-Abelian gauge structures of the Berry connections
(2) Berry connections and their generalization
(3) Quantum order parameters by the Chern numbers and generic Berry phases
(4) Theory of generic Aharnov-Bohm effects
(5) Entanglement entropy of quantum liquids and spin liquids
(6) Universality of the Bulk-Edge correspondence
(7) Characterization of topological orders in quantum liquids


[2] Novel quantum phenomena in real material and their relation to the emerging mathematical concepts as quantum group
Some works [Link1][Link2]
[3] Novel techniques to study ferimonic many body systems with strong correlation
Basic work [Link]
[4] Realistic electronic structures & topological quantities
One of my basic works [Link]


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Institute of Physics
University of Tsukuba
1-1-1 Tennodai
Tsukuba
Ibaraki 305-8571
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A HAPPY NEW YEAR 2020, -299 days left this year !
Recent News
Poster : hatsugai on 2020-11-03 10:00:50 (863 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 (1145 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 (1129 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 (933 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 (1273 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.


    Search
    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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