## 幾何学コロキウム　Classification of Hamiltonians in neighborhoods of band crossings in terms of the theory of singularities

2016年 　 5月 13日 16時 30分 ～ 　 18時 00分

４号館５０１室

アブストラクト：
We classify two-by-two traceless Hamiltonians depending smoothly on a three-dimensional Bloch wavenumber and having a band crossing at the origin of the wavenumber space. In this classification, we regard two such Hamiltonians the equivalent if there are appropriate special unitary transformation of degree 2 and diffeomorphism in the wavenumber space fixing the origin such that one of the Hamiltonians transforms to the other. Based on the equivalence relation, we obtain a complete list of classes up to a codimension 7. For each Hamiltonian in the list, we calculate multiplicity and Chern number, which are invariant under an arbitrary smooth deformation of the Hamiltonian. In addition, we construct a universal unfolding for each Hamiltonian and demonstrate how they can be used for bifurcation analysis of band crossings. We also discuss how the classification changes under certain symmetries relevant for solid state physics and quantum chemistry.

This work is a collaborative work with Prof. Kenji Kondo, Prof. Shyuichi Izumiya, Prof. Mikito Toda and Prof. Tamiki Komatsuzaki.