Year: 2026
Type: preprint
Abstract: We study the edge spectrum of two-dimensional lattice Hamiltonians and magnetic Schrödinger operators in a mobility gap, an energy interval in which the bulk spectrum is potentially localized rather than necessarily absent. Under suitable localization and boundary assumptions, we prove that a constant nonzero bulk topological index implies that the entire interval belongs to the absolutely continuous spectrum of the corresponding half-space operator. The absolutely continuous spectral multiplicity is bounded below by the absolute value of the index at almost every energy in the interval. The first version of the auxiliary-space cut construction in Section 2.3 was generated using ChatGPT 6.
Source: arXiv (Cornell University)
Authors: Becker, Simon, Yang, Mengxuan
Institutions: Bocconi University, Texas A&M University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214044359