Invariable mobility edge in a quasiperiodic lattice

TL;DR

This paper reveals that in a one-dimensional quasiperiodic lattice, the mobility edge remains constant regardless of potential strength, supported by analytical and numerical analysis, with implications for ultracold atom experiments.

Contribution

The study analytically demonstrates an invariable mobility edge in a quasiperiodic lattice, a novel finding contrasting with previous models where the mobility edge varies with potential.

Findings

Critical energy is constant and independent of potential strength.

Wave functions are extended below and localized above the critical energy.

Analytical results are verified through wave function spatial distribution analysis.

Abstract

In this paper, we study a one-dimensional tight-binding model with tunable incommensurate potentials. Through the analysis of the inverse participation rate, we uncover that the wave functions corresponding to the energies of the system exhibit different properties. There exists a critical energy under which the wave functions corresponding to all energies are extended. On the contrary, the wave functions corresponding to all energies above the critical energy are localized. However, we are surprised to find that the critical energy is a constant independent of the potentials. We use the self-dual relation to solve the critical energy, namely the mobility edge, and then we verify the analytical results again by analyzing the spatial distributions of the wave functions. Finally, we give a brief discussion on the possible experimental observation of the invariable mobility edge in the system of ultracold atoms in optical lattices.