# Gap structure of 1D cut and project Hamiltonians

## TL;DR

This paper investigates the gap properties of 1D quasiperiodic Hamiltonians, distinguishing between stable and transient gaps, and establishes a relationship between gap size and gap label, contributing to understanding quasiperiodic systems.

## Contribution

It introduces a classification of gaps into stable and transient and links gap size directly to gap labels in 1D quasiperiodic Hamiltonians.

## Key findings

- Stable gaps have a well-defined quasiperiodic limit.
- A direct relation exists between gap size and gap label.
- Distinction between stable and transient gaps in quasiperiodic chains.

## Abstract

We study the gap properties of nearest neighbors tight binding models on quasiperiodic chains. We argue that two kind of gaps should be distinguished: stable and transient. We show that stable gaps have a well defined quasiperiodic limit. We also show that there is a direct relation between the gap size and the gap label.