The Dry Ten Martini Problem at Criticality

TL;DR

This paper investigates the Dry Ten Martini problem at criticality using advanced methods for constructing quasi-periodic transfer matrices, focusing on the critical almost-Mathieu operator, also known as the Aubry-Andre-Harper model.

Contribution

It introduces new techniques for analyzing the critical almost-Mathieu operator through quasi-periodic transfer matrices, advancing understanding of spectral properties at criticality.

Findings

Successful application of transfer matrix methods to the critical AAH model

Insights into spectral characteristics at the critical point

Potential implications for quasi-periodic systems analysis

Abstract

We apply recently developed methods for the construction of quasi-periodic transfer matrices to the Dry Ten Martini problem for the critical almost-Mathieu Operator, also known as the Aubry-Andre-Harper (AAH) model.