Predicted mobility edges in one-dimensional incommensurate optical lattices: An exactly solvable model of Anderson localization

TL;DR

This paper presents an exactly solvable model for Anderson localization in one-dimensional incommensurate optical lattices, predicting energy-dependent mobility edges and validating them through analytical and numerical methods.

Contribution

It introduces an analytical model with exponential short-range hopping that extends beyond the minimal tight-binding approach, providing explicit predictions for mobility edges.

Findings

Analytical prediction of energy-dependent mobility edges.

Verification of mobility edges through numerical calculations.

Mapping of results to the continuum Schrödinger equation.

Abstract

Localization properties of non-interacting quantum particles in one-dimensional incommensurate lattices are investigated with an exponential short-range hopping that is beyond the minimal nearest-neighbor tight-binding model. Energy dependent mobility edges are analytically predicted in this model and verified with numerical calculations. The results are then mapped to the continuum Schrodinger equation, and an approximate analytical expression for the localization phase diagram and the energy dependent mobility edges in the ground band obtained.