Physical nature of critical wave functions in Fibonacci systems

TL;DR

This paper introduces a new class of critical states in Fibonacci systems, demonstrating their extended nature and linking their spatial structure to quasiperiodic order using a novel transfer matrix renormalization technique.

Contribution

The paper presents a new analytical approach to characterize critical wave functions in Fibonacci systems and establishes their extended transport properties.

Findings

Critical states in Fibonacci systems are extended and spread over the entire system.

A transfer matrix renormalization technique effectively analyzes these states.

The study links the spatial structure of wave functions to quasiperiodic order.

Abstract

We report on a new class of critical states in the energy spectrum of general Fibonacci systems. By introducing a transfer matrix renormalization technique, we prove that the charge distribution of these states spreads over the whole system, showing transport properties characteristic of electronic extended states. Our analytical method is a first step to find out the link between the spatial structure of these critical wave functions and the quasiperiodic order of the underlying lattice.