Tuesday Seminar on Topology

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Date, time & place Tuesday 17:00 - 18:30 056Room #056 (Graduate School of Math. Sci. Bldg.)
Organizer(s) KAWAZUMI Nariya, KITAYAMA Takahiro, SAKASAI Takuya

2017/01/10

18:00-19:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Shin Hayashi (The University of Tokyo)
Topological Invariants and Corner States for Hamiltonians on a Three Dimensional Lattice (JAPANESE)
[ Abstract ]
In condensed matter physics, a correspondence between two topological invariants defined for a gapped Hamiltonian is well-known. One is defined for such a Hamiltonian on a lattice (bulk invariant), and the other is defined for its restriction onto a subsemigroup (edge invariant). The edge invariant is related to the wave functions localized near the edge. This correspondence is known as the bulk-edge correspondence. In this talk, we consider a variant of this correspondence. We consider a periodic Hamiltonian on a three dimensional lattice (bulk) and its restrictions onto two subsemigroups (edges) and their intersection (corner). We will show that, if our Hamiltonian is "gapped" in some sense, we can define a topological invariant for the bulk and edges. We will also define another topological invariant related to the wave functions localized near the corner. We will explain that there is a correspondence between these two topological invariants by using the six-term exact sequence associated to the quarter-plane Toeplitz extension obtained by E. Park.