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Condensed Matter > Mesoscale and Nanoscale Physics
Title: Amoeba Formulation of Non-Bloch Band Theory in Arbitrary Dimensions
(Submitted on 22 Dec 2022 (v1), last revised 30 Apr 2024 (this version, v3))
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.
Submission history
From: Hong-Yi Wang [view email][v1] Thu, 22 Dec 2022 14:34:51 GMT (6596kb,D)
[v2] Thu, 25 Apr 2024 07:14:16 GMT (6593kb,D)
[v3] Tue, 30 Apr 2024 19:29:51 GMT (6594kb,D)
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