Correlated Fermions in a one-dimensional quasiperiodic potential

TL;DR

This paper analyzes how one-dimensional interacting spinless fermions behave in a Fibonacci quasiperiodic potential, revealing a metal-insulator transition influenced by correlations and Fermi level, with unique conductivity properties.

Contribution

It provides an analytical study of the interplay between quasiperiodicity and interactions in fermionic systems, highlighting the transition's dependence on correlation strength and Fermi level.

Findings

Quasiperiodic modulation effects are intermediate between periodic and disordered systems.

A metal-insulator transition depends on correlation strength and Fermi level position.

Conductivity exhibits power-law behavior with non-trivial exponents.

Abstract

We study analytically one-dimensional interacting spinless fermions in a Fibonacci potential. We show that the effects of the quasiperiodic modulation are intermediate between those of a commensurate potential and a disordered one. The system exhibits a metal-insulator transition whose position depends both on the strength of the correlations and on the position of the Fermi level. Consequently, the conductivity displays a power law like size and frequency behaviour characterized by a non trivial exponent.