Remarks on the Spectral Properties of Tight Binding and Kronig-Penney Models with Substitution Sequences

TL;DR

This paper critically examines recent claims about the electronic properties of Thue-Morse models, clarifies the current rigorous mathematical understanding, and discusses unresolved questions in the spectral analysis of substitution sequence models.

Contribution

It clarifies misconceptions in recent studies and reviews the rigorous mathematical results related to spectral properties of substitution sequence models like Thue-Morse.

Findings

Recent claims contradict established theorems

Highlights importance of rigorous mathematical analysis

Identifies open problems and conjectures in the field

Abstract

We comment on some recent investigations on the electronic properties of models associated to the Thue-Morse chain and point out that their conclusions are in contradiction with rigorously proven theorems and indicate some of the sources of these misinterpretations. We briefly review and explain the current status of mathematical results in this field and discuss some conjectures and open problems.