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arXiv · 2212.11743

Amoeba Formulation of Non-Bloch Band Theory in Arbitrary Dimensions

Hong-Yi Wang·Fei Song·Zhong Wang
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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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Hong-Yi Wang, Fei Song, Zhong Wang. 2022-12-22. Amoeba Formulation of Non-Bloch Band Theory in Arbitrary Dimensions. https://doi.org/10.1103/physrevx.14.021011

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