Bulk-entanglement spectrum correspondence in $PT$- and $PC$-symmetric topological insulators and superconductors
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arXiv
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| Format: | Preprint |
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2024
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| author | Takahashi, Ryo Ozawa, Tomoki |
| author_facet | Takahashi, Ryo Ozawa, Tomoki |
| contents | In this study, we discuss a new type of bulk-boundary correspondence which holds for topological insulators and superconductors when the parity-time ($PT$) and/or parity-particle-hole ($PC$) symmetry are present. In these systems, even when the bulk topology is nontrivial, the edge spectrum is generally gapped, and thus the conventional bulk-boundary correspondence does not hold. We find that, instead of the edge spectrum, the single-particle entanglement spectrum becomes gapless when the bulk topology is nontrivial: i.e., the $\textit{bulk-entanglement}$ $\textit{spectrum}$ $\textit{correspondence}$ holds in $PT$- and/or $PC$-symmetric topological insulators and superconductors. After showing the correspondence using $K$-theoretic approach, we provide concrete models for each symmetry class up to three dimensions where nontrivial topology due to $PT$ and/or $PC$ is expected. An implication of our results is that, when the bulk topology under $PT$ and/or $PC$ symmetry is nontrivial, the non-interacting many-body entanglement spectrum is multiply degenerate in one dimension and is gapless in two or higher dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_18372 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bulk-entanglement spectrum correspondence in $PT$- and $PC$-symmetric topological insulators and superconductors Takahashi, Ryo Ozawa, Tomoki Mesoscale and Nanoscale Physics In this study, we discuss a new type of bulk-boundary correspondence which holds for topological insulators and superconductors when the parity-time ($PT$) and/or parity-particle-hole ($PC$) symmetry are present. In these systems, even when the bulk topology is nontrivial, the edge spectrum is generally gapped, and thus the conventional bulk-boundary correspondence does not hold. We find that, instead of the edge spectrum, the single-particle entanglement spectrum becomes gapless when the bulk topology is nontrivial: i.e., the $\textit{bulk-entanglement}$ $\textit{spectrum}$ $\textit{correspondence}$ holds in $PT$- and/or $PC$-symmetric topological insulators and superconductors. After showing the correspondence using $K$-theoretic approach, we provide concrete models for each symmetry class up to three dimensions where nontrivial topology due to $PT$ and/or $PC$ is expected. An implication of our results is that, when the bulk topology under $PT$ and/or $PC$ symmetry is nontrivial, the non-interacting many-body entanglement spectrum is multiply degenerate in one dimension and is gapless in two or higher dimensions. |
| title | Bulk-entanglement spectrum correspondence in $PT$- and $PC$-symmetric topological insulators and superconductors |
| topic | Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2403.18372 |