A generalized eigen value problem, that is described by two hermitian Hamiltonian/overlap matrices, intrisically posesses a conic structure that may induce complex eigen values. The story is geometica...

Various symmetry-protected topological phases of quantum spins on a breathing Pyrochlore are discussed by the Quantum Monte Carlo method. ZN Quantized Berry phases( N=2,3,4,6) are directly evaluated a...

Chiral symmetry in condensed matter physics implies the sublattice symmetry (as far as the one-particle hopping Hamiltonian is concerned). Then the usual belief is that the nearest neighbor hopping Ha...

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...

数理科学 2024年5月号 No.731 (リンク) トポロジカル物質の物理と数理 トポロジーが拓く物質科学の新地平 に記事を書きました。図書館等にてご覧下さい。 量子ホール効果からトポロジカル絶縁体へ ～ トポロジカル相の物理のはじまり ～ 初貝安弘

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...