Invariants for (2+1)D bosonic crystalline topological insulators for all 17 wallpaper groups
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2025
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| author | Calvera, Vladimir Manjunath, Naren Barkeshli, Maissam |
| author_facet | Calvera, Vladimir Manjunath, Naren Barkeshli, Maissam |
| contents | We study bosonic symmetry-protected topological (SPT) phases in (2+1) dimensions with symmetry $G = G_{\text{space}}\times K$, where $G_{\text{space}}$ is a general wallpaper group and $K=\text{U}(1),\mathbb{Z}_N, \text{SO}(3)$ is an internal symmetry. In each case we propose a set of many-body invariants that can detect all the different phases predicted from real space constructions and group cohomology classifications. They are obtained by applying partial rotations and reflections to a given ground state, combined with suitable operations in $K$. The reflection symmetry invariants that we introduce include `double partial reflections', `weak partial reflections' and their `relative' or `twisted' versions which also depend on $K$. We verify our proposal through exact calculations on ground states constructed using real space constructions. We demonstrate our method in detail for the groups p4m and p4g, and in the case of p4m also derive a topological effective action involving gauge fields for orientation-reversing symmetries. Our results provide a concrete method to fully characterize (2+1)D crystalline topological invariants in bosonic SPT ground states. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_26074 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Invariants for (2+1)D bosonic crystalline topological insulators for all 17 wallpaper groups Calvera, Vladimir Manjunath, Naren Barkeshli, Maissam Strongly Correlated Electrons Mesoscale and Nanoscale Physics High Energy Physics - Theory Quantum Physics We study bosonic symmetry-protected topological (SPT) phases in (2+1) dimensions with symmetry $G = G_{\text{space}}\times K$, where $G_{\text{space}}$ is a general wallpaper group and $K=\text{U}(1),\mathbb{Z}_N, \text{SO}(3)$ is an internal symmetry. In each case we propose a set of many-body invariants that can detect all the different phases predicted from real space constructions and group cohomology classifications. They are obtained by applying partial rotations and reflections to a given ground state, combined with suitable operations in $K$. The reflection symmetry invariants that we introduce include `double partial reflections', `weak partial reflections' and their `relative' or `twisted' versions which also depend on $K$. We verify our proposal through exact calculations on ground states constructed using real space constructions. We demonstrate our method in detail for the groups p4m and p4g, and in the case of p4m also derive a topological effective action involving gauge fields for orientation-reversing symmetries. Our results provide a concrete method to fully characterize (2+1)D crystalline topological invariants in bosonic SPT ground states. |
| title | Invariants for (2+1)D bosonic crystalline topological insulators for all 17 wallpaper groups |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2510.26074 |