Z3 Berry phases for XXZ quantum spins on Kagome lattice are calculated by the quantum Monte Carlo method under a condition with fixed magnetization. The phase diagram of the model is discussed by usin...

Spatial variation of physical parameters may induce rich phenomena, which can only be realized in artificial structures by meta-materials and cold atoms. Non-uniform flux associated with particle bloc...

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 ...

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.

I have written an article for JPSJ News & Comments. Have a look at "Nontrivial Topology of Nontopological Nonlinear Waves." See also old ones. "Y. Hatsugai, News Comments 20, 10 (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 ...

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...

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...

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 intege...

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...

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...

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...

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 possibiliti...

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 f...

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...