Many aspects of non-Hermitian systems are not well described in the framework of Bloch band theory. The non-Bloch band theory, in which the concept of Brillouin zone is generalized, has been widely applied to study non-Hermitian systems in one spatial dimension. However, its generalization to higher dimensions has been challenging. Here, we introduce a formulation of non-Hermitian band theory in arbitrary spatial dimensions, which is based on a natural geometrical object known as the amoeba. This 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.
Reference: H.-Y. Wang, F. Song, Z. Wang, arXiv:2212.11743