Systematic Construction of Interfaces and Anomalous Boundaries for Fermionic Symmetry-Protected Topological Phases
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913846456745984 |
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| author | Loo, Kevin Wang, Qing-Rui |
| author_facet | Loo, Kevin Wang, Qing-Rui |
| contents | We use the pullback trivialization technique to systematically construct gapped interfaces and anomalous boundaries for fermionic symmetry-protected topological (FSPT) states by extending their symmetry group $G_f = \mathbb{Z}_2^f \times_{ω_2} G$ to larger groups. These FSPT states may involve decoration layers of both Majorana chains and complex fermions. We derive general consistency formulas explicitly for (2+1)D and (3+1)D systems, where nontrivial twists arise from fermionic symmetric local unitaries or "gauge transformations" that ensure coboundaries vanish at the cochain level. Additionally, we present explicit example for a (3+1)D FSPT of symmetry group $G_f=\mathbb{Z}_2^f \times \mathbb{Z}_4 \times \mathbb{Z}_4$ with Majorana chain decorations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_18528 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Systematic Construction of Interfaces and Anomalous Boundaries for Fermionic Symmetry-Protected Topological Phases Loo, Kevin Wang, Qing-Rui Strongly Correlated Electrons High Energy Physics - Theory We use the pullback trivialization technique to systematically construct gapped interfaces and anomalous boundaries for fermionic symmetry-protected topological (FSPT) states by extending their symmetry group $G_f = \mathbb{Z}_2^f \times_{ω_2} G$ to larger groups. These FSPT states may involve decoration layers of both Majorana chains and complex fermions. We derive general consistency formulas explicitly for (2+1)D and (3+1)D systems, where nontrivial twists arise from fermionic symmetric local unitaries or "gauge transformations" that ensure coboundaries vanish at the cochain level. Additionally, we present explicit example for a (3+1)D FSPT of symmetry group $G_f=\mathbb{Z}_2^f \times \mathbb{Z}_4 \times \mathbb{Z}_4$ with Majorana chain decorations. |
| title | Systematic Construction of Interfaces and Anomalous Boundaries for Fermionic Symmetry-Protected Topological Phases |
| topic | Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2412.18528 |