(2+1)D topological phases with RT symmetry: many-body invariant, classification, and higher order edge modes
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| Format: | Preprint |
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2024
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| _version_ | 1866917120339607552 |
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| author | Kobayashi, Ryohei Zhang, Yuxuan Wang, Yan-Qi Barkeshli, Maissam |
| author_facet | Kobayashi, Ryohei Zhang, Yuxuan Wang, Yan-Qi Barkeshli, Maissam |
| contents | It is common in condensed matter systems for reflection ($R$) and time-reversal ($T$) symmetry to both be broken while the combination $RT$ is preserved. In this paper we study invariants that arise due to $RT$ symmetry. We consider many-body systems of interacting fermions with fermionic symmetry groups $G_f = \mathbb{Z}_2^f \times \mathbb{Z}_2^{RT}$, $U(1)^f \rtimes \mathbb{Z}_2^{RT}$, and $U(1)^f \times \mathbb{Z}_2^{RT}$. We show that (2+1)D invertible fermionic topological phases with these symmetries have a $\mathbb{Z} \times \mathbb{Z}_8$, $\mathbb{Z}^2 \times \mathbb{Z}_2$, and $\mathbb{Z}^2 \times \mathbb{Z}_4$ classification, respectively, which we compute using the framework of $G$-crossed braided tensor categories. We provide a many-body $RT$ invariant in terms of a tripartite entanglement measure, and which we show can be understood using an edge conformal field theory computation in terms of vertex states. For $G_f = U(1)^f \rtimes \mathbb{Z}_2^{RT}$, which applies to charged fermions in a magnetic field, the non-trivial value of the $\mathbb{Z}_2$ invariant requires strong interactions. For symmetry-preserving boundaries, the phases are distinguished by zero modes at the intersection of the reflection axis and the boundary. Additional invariants arise in the presence of translation or rotation symmetry. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_18887 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | (2+1)D topological phases with RT symmetry: many-body invariant, classification, and higher order edge modes Kobayashi, Ryohei Zhang, Yuxuan Wang, Yan-Qi Barkeshli, Maissam Strongly Correlated Electrons Mesoscale and Nanoscale Physics High Energy Physics - Theory Quantum Physics It is common in condensed matter systems for reflection ($R$) and time-reversal ($T$) symmetry to both be broken while the combination $RT$ is preserved. In this paper we study invariants that arise due to $RT$ symmetry. We consider many-body systems of interacting fermions with fermionic symmetry groups $G_f = \mathbb{Z}_2^f \times \mathbb{Z}_2^{RT}$, $U(1)^f \rtimes \mathbb{Z}_2^{RT}$, and $U(1)^f \times \mathbb{Z}_2^{RT}$. We show that (2+1)D invertible fermionic topological phases with these symmetries have a $\mathbb{Z} \times \mathbb{Z}_8$, $\mathbb{Z}^2 \times \mathbb{Z}_2$, and $\mathbb{Z}^2 \times \mathbb{Z}_4$ classification, respectively, which we compute using the framework of $G$-crossed braided tensor categories. We provide a many-body $RT$ invariant in terms of a tripartite entanglement measure, and which we show can be understood using an edge conformal field theory computation in terms of vertex states. For $G_f = U(1)^f \rtimes \mathbb{Z}_2^{RT}$, which applies to charged fermions in a magnetic field, the non-trivial value of the $\mathbb{Z}_2$ invariant requires strong interactions. For symmetry-preserving boundaries, the phases are distinguished by zero modes at the intersection of the reflection axis and the boundary. Additional invariants arise in the presence of translation or rotation symmetry. |
| title | (2+1)D topological phases with RT symmetry: many-body invariant, classification, and higher order edge modes |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2403.18887 |