Bulk-edge correspondence for energy dependent systems/nonlinear eigen value problems

Bulk-edge correspondence for energy dependent systems/nonlinear eigen value problems

The recent development of a topological description of matter, especially for classical systems, is based on the formal analogy to quantum mechanics. The differential equation governing the classical ...
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Bulk-edge correspondence (Encyclopedia of condensed matter physics, 2nd Ed.)

Bulk-edge correspondence (Encyclopedia of condensed matter physics, 2nd Ed.)

I wrote a chapter on the bulk-edge correspondence in Encyclopedia of condensed matter physics, 2nd Ed.,Volume 1, 2024, Pages 659-669, Its abstract is free.
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Nontrivial Topology of Nontopological Nonlinear Waves

Nontrivial Topology of Nontopological Nonlinear Waves

I have written an article for JPSJ News & Comments. Have a look at "Nontrivial Topology of Nontopological Nonlinear Waves." See also old ones.
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Heat carrying corner states of breathing Kagome

Heat carrying corner states of breathing Kagome

Heat conduction of the breathing Kagome lattice is discussed in relation to the anomalous heat-carrying corner states due to higher-order topology. Especially the use of the effective Hamiltonian for ...
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Z2× Z2 symmetry and Z4 quantization in bosonic ladders

Z2× Z2 symmetry and Z4 quantization in bosonic ladders

A two-leg ladder is a nice place to discuss Z2× Z2 symmetry with sufficient numerical accuracy. Using a Z4 Berry phases, several phases of bosonic ladders are discussed in relation to the bulk-edge co...
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Negative index photonic crystal induces non hermitian physics

Negative index photonic crystal induces non hermitian physics

An electromagnetic field in a photonic crystal is described by a hermitian eigenvalue problem with an overlap matrix which may not be positive definite if the system is composed of negative index medi...
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Diophantine equation of SU(Q) topological pump

Diophantine equation of SU(Q) topological pump

A topological pump of SU(Q) interacting fermions is proposed based on Affleck's SU(Q) quantum chains associated with a symmetric breaking term characterized by a parameter P/Q with co-prime integers P...
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Graphene, silicene and martini

Graphene, silicene and martini

Chemisorption on graphene and silicene may realize Martini type π-electron network. It implies specific band dispersion. We propose potential materialization by using the molecular orbital constr...
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Array of Martini glasses with topology

Array of Martini glasses with topology

Taking a square root is not trivial. The Dirac equation is invented by the square root of the Kleind-Gordon equation. Then the lattice analog of the operation implies non-trivial topology and edge/cor...
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Novel critical states in random U(1) MO models in 2D

Novel critical states in random U(1) MO models in 2D

Using a molecular orbital (MO) construction scheme of the flat band which we are proposing, we found novel random critical states in a series of flat band systems away from the flat band energy. The M...
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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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