SPT indices emerging from translation invariance in two dimensional quantum spin systems
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866913249136476160 |
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| author | Jappens, Tijl |
| author_facet | Jappens, Tijl |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_11758 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | SPT indices emerging from translation invariance in two dimensional quantum spin systems Jappens, Tijl Mathematical Physics Statistical Mechanics Quantum Physics 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. |
| title | SPT indices emerging from translation invariance in two dimensional quantum spin systems |
| topic | Mathematical Physics Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2202.11758 |