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arXiv · 2401.00050

Many-body higher-order topological invariant for $C_n$-symmetric insulators

Ammar Jahin·Yuan-Ming Lu·Yuxuan Wang
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Abstract

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.

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Ammar Jahin, Yuan-Ming Lu, Yuxuan Wang. 2023-12-29. Many-body higher-order topological invariant for $C_n$-symmetric insulators. https://arxiv.org/abs/2401.00050

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