Many-body higher-order topological invariant for $C_n$-symmetric insulators
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866916083229786112 |
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| author | Jahin, Ammar Lu, Yuan-Ming Wang, Yuxuan |
| author_facet | Jahin, Ammar Lu, Yuan-Ming Wang, Yuxuan |
| contents | Higher-order topological insulators in two spatial dimensions display fractional corner charges. While fractional charges in one dimension are known to be captured by a many-body bulk invariant, computed by the Resta formula, a many-body bulk invariant for higher-order topology and the corresponding fractional corner charges remains elusive despite several attempts. Inspired by recent work by Tada and Oshikawa, we propose a well-defined many-body bulk invariant for $C_n$ symmetric higher-order topological insulators, which is valid for both non-interacting and interacting systems. Instead of relating them to the bulk quadrupole moment as was previously done, we show that in the presence of $C_n$ rotational symmetry, this bulk invariant can be directly identified with quantized fractional corner charges. In particular, we prove that the corner charge is quantized as $e/n$ with $C_n$ symmetry, leading to a $\mathbb{Z}_n$ classification for higher-order topological insulators in two dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_00050 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Many-body higher-order topological invariant for $C_n$-symmetric insulators Jahin, Ammar Lu, Yuan-Ming Wang, Yuxuan Strongly Correlated Electrons Mesoscale and Nanoscale Physics Higher-order topological insulators in two spatial dimensions display fractional corner charges. While fractional charges in one dimension are known to be captured by a many-body bulk invariant, computed by the Resta formula, a many-body bulk invariant for higher-order topology and the corresponding fractional corner charges remains elusive despite several attempts. Inspired by recent work by Tada and Oshikawa, we propose a well-defined many-body bulk invariant for $C_n$ symmetric higher-order topological insulators, which is valid for both non-interacting and interacting systems. Instead of relating them to the bulk quadrupole moment as was previously done, we show that in the presence of $C_n$ rotational symmetry, this bulk invariant can be directly identified with quantized fractional corner charges. In particular, we prove that the corner charge is quantized as $e/n$ with $C_n$ symmetry, leading to a $\mathbb{Z}_n$ classification for higher-order topological insulators in two dimensions. |
| title | Many-body higher-order topological invariant for $C_n$-symmetric insulators |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2401.00050 |