Quantum and Spectral Properties of the Labyrinth Model

TL;DR

This paper investigates the spectral and density of states properties of the Labyrinth quasicrystal model, revealing that its spectrum becomes an interval and the density of states measure is absolutely continuous at small coupling.

Contribution

It demonstrates that the spectrum of the Labyrinth model transitions from a Cantor set product to an interval and the density of states measure becomes absolutely continuous in the small coupling regime.

Findings

Spectrum is an interval for small coupling constants.

Density of states measure is absolutely continuous for almost all small couplings.

Spectral properties depend on the coupling strength.

Abstract

We consider the Labyrinth model, which is a two-dimensional quasicrystal model. We show that the spectrum of this model, which is known to be a product of two Cantor sets, is an interval for small values of the coupling constant. We also consider the density of states measure of the Labyrinth model, and show that it is absolutely continuous with respect to Lebesgue measure for almost all values of coupling constants in small coupling regime.