One of the recent wisdom for topological phases is the use of a classical system as a quantum simulator. The Hofstadter butterfly associated with topological phase transitions is realized in electric ...

Adiabatic connection of the gapped many-body states is a conceptual background of the topological phases. Historical and more than successful examples are given by various fractional quantum Hall stat...

The discriminant is a generalization of the　"b 2- 4 ac" formula that everybody knows, which tells us the degeneracy of the (secular) equation. Then it is natural the discriminant is useful f...

Analyzing a diffusion equation of alternative metals, rapid heat conduction to the heat bath due to edge states is predicted. The edge states are predicted by the bulk topological invariant as a typic...

As widely accepted, the degeneracy of eigenvalues of the Hamiltonian is a singular point, which is the source of the non-trivial topology. Then it is more than natural that the discriminant of the sec...

The Haldane model with Kekulè distortion possesses various phases characterized by different topology with specific boundary states. Competition between the 1st/2nd order topology (1D/0D boundary stat...

Generic degeneracy of a non-hermitian hamiltonian implies a set of the eigenvectors is not enough to span the total linear space. One needs to extend the idea of the eigenstates to the generic ones, w...

Topological (adiabatic) pumps are typical problems where the bulk-edge correspondence is justified. The Chern number of the bulk and the behavior of the edge states are linked intimately. As for most ...