Diophantine equation of SU(Q) topological pump
hatsugai
/ 2023年5月6日
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年2月22日
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年2月22日
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年2月22日
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年1月26日
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年11月28日
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年9月29日
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年7月29日
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年6月2日
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年4月6日
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年2月25日
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年2月20日
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年2月18日
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年1月21日
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年1月11日
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年12月28日
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
hatsugai
/ 2021年10月26日
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
hatsugai
/ 2021年10月14日
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
hatsugai
/ 2021年9月10日
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
hatsugai
/ 2021年8月19日
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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