Symmetry-protected quantization of complex Berry phases in non-Hermitian many-body systems
| Autor: | Tsubota, Shoichi, Yang, Hong, Akagi, Yutaka, Katsura, Hosho |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Phys. Rev. B 105, L201113 (2022) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevB.105.L201113 |
| Popis: | We investigate the quantization of the complex-valued Berry phases in non-Hermitian quantum systems with certain generalized symmetries. In Hermitian quantum systems, the real-valued Berry phase is known to be quantized in the presence of certain symmetries, and this quantized Berry phase can be regarded as a topological order parameter for gapped quantum systems. In this paper, on the other hand, we establish that the complex Berry phase is also quantized in the systems described by a family of non-Hermitian Hamiltonians. Let $H(\theta)$ be a non-Hermitian Hamiltonian parameterized by $\theta$. Suppose that there exists a unitary and Hermitian operator $P$ such that $PH(\theta)P = H(-\theta)$ or $PH(\theta)P = H^\dagger(-\theta)$. We prove that in the former case, the complex Berry phase $\gamma$ is $\mathbb{Z}_2$-quantized, while in the latter, only the real part of $\gamma$ is $\mathbb{Z}_2$-quantized. The operator $P$ can be viewed as a generalized symmetry for $H(\theta)$, and in practice, $P$ can be, for example, a spatial inversion. We also argue that this quantized complex Berry phase is capable of classifying non-Hermitian topological phases, and we demonstrate this in some one-dimensional strongly correlated systems. Comment: 6 pages, 4 figures |
| Databáze: | arXiv |
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