Exact new mobility edges

TL;DR

This paper identifies two exact new mobility edges in realistic quantum models, distinguishing critical, localized, and extended states through spectral analysis of singular Jacobi operators.

Contribution

It introduces two novel types of mobility edges, expanding understanding of phase transitions in quantum systems with rigorous spectral analysis.

Findings

Existence of Type II and Type III mobility edges

Critical energies separating different quantum states

Spectral analysis confirms the mobility edges

Abstract

Mobility edges (ME), defined as critical energies that separate the extended states from the localized states, are a significant topic in quantum physics. In this paper, we demonstrate the existence of two exact new mobility edges for two physically realistic models: the first, referred to as Type II ME, represents the critical energy that separates the critical states from localized states; the second, referred to as Type III ME, marks the critical energy that separate the critical states from extended states. The proof is based on spectral analysis of singular Jacobi operator on the strip.