The Creation of Spectral Gaps by Graph Decoration

TL;DR

This paper introduces a method called graph decoration to create spectral gaps in self-adjoint operators on graphs, relevant for understanding spectral properties of discrete models with local structures.

Contribution

It proposes a novel graph decoration technique to induce spectral gaps in operators, advancing the control of spectral properties in graph-based models.

Findings

Spectral gaps can be generated through graph decoration.

The method applies to operators with local structural features.

Potential applications in designing materials with specific spectral properties.

Abstract

We present a mechanism for the creation of gaps in the spectra of self-adjoint operators defined over a Hilbert space of functions on a graph, which is based on the process of graph decoration. The resulting Hamiltonians can be viewed as associated with discrete models exhibiting a repeated local structure and a certain bottleneck in the hopping amplitudes.