Amoeba Formulation of Non-Bloch Band Theory in Arbitrary Dimensions

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.

21 pages, 11 figures, 1 table

References in corpus (6)

• Topological Origin of Non-Hermitian Skin Effects
• Non-Hermitian Topology and Exceptional-Point Geometries
• Non-Hermitian Morphing of Topological Modes
• Non-Bloch topological invariants in a non-Hermitian domain-wall system
• Liouvillian Skin Effect in an Exactly Solvable Model
• Scaling rule in critical non-Hermitian skin effect

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