## Nontrivial Topology of Nontopological Nonlinear Waves

hatsugai
/ 2023.8.22

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

hatsugai
/ 2023.7.20

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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##
Z_{2}× Z_{2} symmetry and Z_{4} quantization in bosonic ladders

hatsugai
/ 2023.7.14

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

hatsugai
/ 2023.6.15

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

hatsugai
/ 2023.6.2

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

hatsugai
/ 2023.2.22

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

hatsugai
/ 2023.2.22

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

hatsugai
/ 2023.2.22

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

hatsugai
/ 2023.1.26

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

hatsugai
/ 2022.11.28

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

hatsugai
/ 2022.9.29

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

hatsugai
/ 2022.7.29

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

hatsugai
/ 2022.6.2

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

hatsugai
/ 2022.4.6

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

hatsugai
/ 2022.2.25

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

hatsugai
/ 2022.2.20

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

hatsugai
/ 2022.2.18

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

hatsugai
/ 2022.1.21

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

hatsugai
/ 2022.1.11

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

hatsugai
/ 2021.12.28

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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