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Symmetry and Topology in Non-Hermitian Physics
Kohei Kawabata, Ken Shiozaki, Masahito Ueda +1
We develop a complete theory of symmetry and topology in non-Hermitian physics. We demonstrate that non-Hermiticity ramifies the celebrated Altland-Zirnbauer symmetry classificatio…
Many-Body Order Parameters for Multipoles in Solids
Byungmin Kang, Ken Shiozaki, Gil Young Cho
We propose many-body order parameters for bulk multipoles in crystalline systems, which originate from the non-trivial topology of the nested Wilson loop spectrum. The many-body or…
Classification of topological crystalline superconducting nodes on high-symmetry lines: Point nodes, line nodes, and Bogoliubov Fermi surfaces
Shuntaro Sumita, Takuya Nomoto, Ken Shiozaki +1
Recent development in exact classification of a superconducting gap has elucidated various unconventional gap structures, which have not been predicted by the classification of ord…
Glide-symmetric magnetic topological crystalline insulators with inversion symmetry
Heejae Kim, Ken Shiozaki, Shuichi Murakami
It is known that three-dimensional magnetic systems with glide symmetry can be characterized by a topological invariant together with the Chern number associated with the nor…
Topological classification under nonmagnetic and magnetic point group symmetry: Application of real-space Atiyah-Hirzebruch spectral sequence to higher-order topology
Nobuyuki Okuma, Masatoshi Sato, Ken Shiozaki
We classify time-reversal breaking (class A) spinful topological crystalline insulators with crystallographic non-magnetic (32 types) and magnetic (58 types) point groups. The clas…
Generalized homology and Atiyah-Hirzebruch spectral sequence in crystalline symmetry protected topological phenomena
Ken Shiozaki, Charles Zhaoxi Xiong, Kiyonori Gomi
We propose that symmetry protected topological (SPT) phases with crystalline symmetry are formulated by equivariant generalized homologies over a real space manifold …
Anomalous helical edge states in a non-Hermitian Chern insulator
Kohei Kawabata, Ken Shiozaki, Masahito Ueda
A non-Hermitian extension of a Chern insulator and its bulk-boundary correspondence are investigated. It is shown that in addition to the robust chiral edge states that reflect the…
Lieb-Schultz-Mattis type theorem with higher-form symmetry and the quantum dimer models
Ryohei Kobayashi, Ken Shiozaki, Yuta Kikuchi +1
The Lieb-Schultz-Mattis theorem dictates that a trivial symmetric insulator in lattice models is prohibited if lattice translation symmetry and charge conservation are both…
Atiyah-Hirzebruch Spectral Sequence in Band Topology: General Formalism and Topological Invariants for 230 Space Groups
Ken Shiozaki, Masatoshi Sato, Kiyonori Gomi
We study the Atiyah-Hirzebruch spectral sequence (AHSS) for equivariant K-theory in the context of band theory. Various notions in the band theory such as irreducible representatio…