Non-Bloch band theory of nonlinear eigenvalue problems

Abstract

Nonlinear eigenvalue problems arise in a wide range of physical systems, in which system parameters depend on the eigenvalue. Such systems have been proposed to exhibit an extreme sensitivity of their spectra to boundary conditions, which leads to the breakdown of conventional topological characterizations. In this work, we establish a non-Bloch framework for calculating continuum bands that reproduce the spectra of the nonlinear system with open boundary conditions. This non-Bloch band theory enables us not only to calculate the eigenvalues but also to reveal phenomena unique to the nonlinear system. We further investigate the topological bulk-boundary correspondence in a nonlinear Chern insulator within an extended version of this framework.