ZQ Berry phase, that is quantized due to symmetry, is defined and used successfully for characterization of 2D/3D higher order topological phases with/without interaction. Both for spins and fermions. The article by Hiromu Araki, Tomonari Mizoguchi and Yasuhiro Hatsugai has been published in Physical Review Research. Also it is highlighted here as one of the Rapid Communications. Have a look at !
We have discussed a non-hermitian version of the fractional quantum Hall states. The paper, by Tsuneya Yoshida, Koji Kudo and Yasuhiro Hatsugai, has been published in Scientific Reports ( also arXiv:1907.07596 ). Non-hermitian physics has been extended to the topologically ordered states. It's a try. Relevant situations can be realized in cold atom experiments.
Covalent Organic Frameworks (COF), I understand, is a large molecule where many (block) organic molecules are linked by strong covalent bonds in a periodic or non-periodic manner. It is a nice place where the higher order topological insulating phase is realized as we have pointed out. Then if the COF has boundaries, one can naturally expect edge states/corner states associated with the symmetry protected Berry phases of the bulk. This is correct. One of such a COF, we discussed, is a polymerized triptycene on a decorated star lattice. Our paper ”Flat bands and higher-order topology in polymerized triptycene: Tight-binding analysis on decorated star lattices” by Tomonari Mizoguchi, Mina Maruyama, Susumu Okada, Yasuhiro Hatsugai is for the phenomena and has been published in Physical Review Materials (See also arXiv 1907.06088).
We have proposed a new correlated topological phase, "higher-order topological Mott insulator (HOTMI)" where spin-charge separated corner states emerge that are protected by Z3 spin Berry phases of the bulk. It is a generalized bulk-edge correspondence. The article has been published in Phys. Rev. Lett. (also arXiv:1905.03484). Have a look at.
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 non-orthogonal 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, "Molecular-orbital representation of generic flat-band models", by T. Mizoguchi and Y. Hatsugai , also arXiv.
I wrote a small article "So Small Implies So Large: For a Material Design" in the "News and comment" section of the JPSJ in relation to a recent interesting paper by Toshikaze Kariyado. Material deformation induces a gauge field that modifies electronic structure and may result in the Landau levels without breaking time reversal. Have a look at.
Our paper "Higher-Order Topological Phase in a Honeycomb-Lattice Model with Anti-Kekulé Distortion" by Tomonari Mizoguchi, Hiromu Araki, and Yasuhiro Hatsugai, has appeared in J. Phys. Soc. Jpn. 88, 104703 (2019). One can access also via arXiv:1906.07928. Z6 quantization in honeycomb structure is the key. Have a look at.
Due to an intrinsic symmetry of a mechanical system with friction governed by the Newton equation, exceptional rings appear in two dimensions. We have demonstrated it and classification of symmetry-protected non-Hermitian degeneracies is addressed putting a focus on the symmetry. The paper is published in Physical Review B, "Exceptional rings protected by emergent symmetry for mechanical systems" by Tsuneya Yoshida and Yasuhiro Hatsugai. You may find also here arXiv:1904.10764.
A series of quantum phase transitions of integer Heisenberg spin chains (S=2, 3 and 4) with J1-J2 interaction is characterized by the Z2 Berry phases associated with local U(1) bond twists. The results are consistently understood by the valence bond (VB) reconstruction and adiabatic deformation to the generalized AKLT models. Have a look at, arXiv:1904.00612 and Phys. Rev. B 100, 014438 (2019) (published).
Our paper, "Fractionally Quantized Berry’s Phase in an Anisotropic Magnet on the Kagome Lattice" by T. Kawarabayashi, K. Ishi and Y.Hatsugai, has been published in JPSJ (arXiv:1806.10767). 
Z3 Berry phases characterize "Trimer phase" of quantum S=1/2 spins on a Kagome lattice.
