Topological protection of singularities for the non-Hermitian problem is one of the recent focuses in condensed matter physics. Exceptional points and rings with symmetry constraints are typical examp...

Topological protection for topological systems may change by the inclusion of particle-particle interaction, which is known as "reduction phenomena." Here we have pointed out its possibilities for 1-d...

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 for the stu...

Recent wisdom for the construction of flat bands is applicable even with randomness. Characterization of special features of the random flat bands has been successfully done by using machine learning....

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...

Once one admits the electronic state is described by the molecular-orbitals (MOs), the system has flat bands when the number of MOs is less than the total number of atoms. Then it is natural the elect...

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 use of topological invariants for the characterization of material phases has been quite successful. Non-trivial topology is reflected by physical observables near the boundaries of systems as a b...

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...

Adiabatic insertion of the Aharonov-Bohm flux through two pinholes introduces charge transport between them when the system is topologically non-trivial. This is the Laughlin argument. The defects/pin...

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...

Corner states of the breezing Pyrochlore lattice are protected by the Z4 symmetry as a typical example of the bulk-edge/boundary correspondence using Z4 Berry phase. With on-site Coulomb interaction, ...

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 ...

Eigenvalues may not be always real for generalized eigenvalue problems even if the Hamiltonian and overlap matrices are both Hermitian. When the overlap is associated with a norm of physical state, th...

A flat band system with interaction that possesses a single "quantum scar", which we have proposed in Kuno-Mizoguchi-Hatsugai, Phys. Rev. B 102, 241115(R) (2020), is extended to a system with multiple...

Bulk-edge correspondence is universal. We do find a novel playground of the chiral edge states protected by bulk topology. It is in the evolutionary game theory realized in a kagome network. The paper...

Covalent/Metal-organic framework (COF/MOF) is a 2D/3D network compound of organic molecules (linkages) connected by linker molecules. This material possesses a set of flat bands (at least in a tight-b...

We are proposing one more lattice structure with frustration that hosts flat bands, square-Kagome lattice. Using a molecular orbital representation, its flat band and flat dispersion only in some spec...