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arXiv · 2202.11758

SPT indices emerging from translation invariance in two dimensional quantum spin systems

Tijl Jappens
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Abstract

We consider SPT-phases with on-site $G$ (where $G$ is any finite group) symmetry for two-dimensional quantum spin systems. We then impose translation invariance in one direction and observe that on top of the $H^3(G,\mathbb{T})$-valued index constructed in \cite{ogata2021h3gmathbb}, an additional $H^2(G,\mathbb{T})$-valued index emerges. We also show that if we impose translation invariance in two directions, on top of the expected $H^3(G,\mathbb{T})\oplus H^2(G,\mathbb{T})\oplus H^2(G,\mathbb{T})$ valued index, an additional $H^1(G,\mathbb{T})$-valued index emerges.

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Tijl Jappens. 2022-02-23. SPT indices emerging from translation invariance in two dimensional quantum spin systems. https://doi.org/10.1007/s00220-023-04875-7

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