Amoeba Formulation of Non-Bloch Band Theory in Arbitrary Dimensions

• URL: http://arxiv.org/abs/2212.11743v3
• Date: Tue, 30 Apr 2024 19:29:51 GMT
• Title: Amoeba Formulation of Non-Bloch Band Theory in Arbitrary Dimensions
• Authors: Hong-Yi Wang, Fei Song, Zhong Wang,
• Abstract summary: We develop a formulation of the non-Hermitian skin effect and non-Bloch band theory in arbitrary spatial dimensions. Key quantities of non-Hermitian bands, including the energy spectrum, eigenstates profiles, and the generalized Brillouin zone, can be efficiently obtained from this approach.
• Score: 9.924017206241272
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The non-Hermitian skin effect dramatically reshapes the energy bands of non-Hermitian systems, meaning that the usual Bloch band theory is fundamentally inadequate as their characterization. The non-Bloch band theory, in which the concept of Brillouin zone is generalized, has been widely applied to investigate non-Hermitian systems in one spatial dimension. However, its generalization to higher dimensions has been challenging. Here, we develop a formulation of the non-Hermitian skin effect and non-Bloch band theory in arbitrary spatial dimensions, which is based on a natural geometrical object known as the amoeba. Our theory provides a general framework for studying non-Hermitian bands beyond one dimension. Key quantities of non-Hermitian bands, including the energy spectrum, eigenstates profiles, and the generalized Brillouin zone, can be efficiently obtained from this approach.

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