Topological strucure can be fragile against interactions

Topological strucure can be fragile against interactions

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...
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Reduction of non-Hermitian 1D topology with interaction

Reduction of non-Hermitian 1D topology with interaction

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...
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Bulk-edge correspondence in electric circuits of topological pump

Bulk-edge correspondence in electric circuits of topological pump

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 ...
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Adiabatic connection with spin

Adiabatic connection with spin

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...
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“b 2– 4 ac” formula with rotation symmetry

“b 2– 4 ac” formula with rotation symmetry

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...
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Random flatbands are special

Random flatbands are special

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....
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Heat escapes fast due to bulk-edge correspondence

Heat escapes fast due to bulk-edge correspondence

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...
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Exact correlation of correlation

Exact correlation of correlation

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...
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Discriminant and symmetry

Discriminant and symmetry

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...
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Non Hermitian topology in game theory

Non Hermitian topology in game theory

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...
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First/second order topology in honeycomb lattice

First/second order topology in honeycomb lattice

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...
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Flux attachement and bulk-edge correspondence

Flux attachement and bulk-edge correspondence

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...
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Multi-fold EP protected by anti-unitary symmetry

Multi-fold EP protected by anti-unitary symmetry

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...
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3D HOTI of Hubbard model by  negative sign free quantum Monte Carlo

3D HOTI of Hubbard model by negative sign free quantum Monte Carlo

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, ...
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Bulk-edge correspondence of interacting bosonic pump

Bulk-edge correspondence of interacting bosonic pump

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 ...
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Non real energies for Hermitian problems

Non real energies for Hermitian problems

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...
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Multiple quantum scars and dynamics

Multiple quantum scars and dynamics

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...
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One more topological phase with chiral edge states

One more topological phase with chiral edge states

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...
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Flat bands of COF/MOF in any dimension

Flat bands of COF/MOF in any dimension

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...
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Flat bands and spin-1 Dirac cone

Flat bands and spin-1 Dirac cone

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...
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