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A discrete formulation of the Kane-Mele invariant
Ken Shiozaki
We present a discrete formulation of the Kane-Mele invariant that is manifestly gauge-independent and quantized.
Higher Berry curvature from matrix product states
Ken Shiozaki, Niclas Heinsdorf, Shuhei Ohyama
The higher Berry curvature was introduced by Kapustin and Spodyneiko as an extension of the Berry curvature in quantum mechanical systems with finite degrees of freedom to quantum…
Discrete Higher Berry Phases and Matrix Product States
Shuhei Ohyama, Yuji Terashima, Ken Shiozaki
A -parameter family of invertible states gives a topological transport phenomenon, similar to the Thouless pumping. As a natural generalization of this, we can consider a family…
Atiyah-Hirzebruch spectral sequence for topological insulators and superconductors: pages for 1651 magnetic space groups
Ken Shiozaki, Seishiro Ono
We compute the pages of the momentum-space and real-space Atiyah-Hirzebruch spectral sequence (AHSS) for topological crystalline insulators and superconductors up to three sp…