A $H^3(G,\mathbb{T})$-valued index of symmetry protected topological phases with on-site finite group symmetry for two-dimensional quantum spin systems

Abstract

We consider SPT-phases with on-site finite group $G$ symmetry $\beta$ for two-dimensional quantum spin systems. We show that they have $H^3(G,\mathbb{T})$-valued invariant.

The present result and the main idea of the proof were announced publicly on 15 Dec 2020 at IAMP One World Mathematical Physics Seminar (see you-tube video https://youtu.be/cXk6Fk5wD_4), also at an international meeting Theoretical studies of topological phases of matter on 17 Dec 2020, and Current Developments in Mathematics 4th Jan 2021 via zoom with a lecture note

Cited by in corpus (3)

• An index for two-dimensional SPT states
• The split and approximate split property in 2D systems: stability and absence of superselection sectors
• An invariant of symmetry protected topological phases with on-site finite group symmetry for two-dimensional Fermion systems