Self-consistent theory of mobility edges in quasiperiodic chains

TL;DR

This paper develops a self-consistent, model-independent theoretical framework to analytically determine mobility edges in quasiperiodic chains, distinguishing localized from extended states, and validates it with specific models and numerical results.

Contribution

The authors introduce a novel, analytical, and model-independent theory for mobility edges in quasiperiodic systems, extending beyond the Aubry-André-Harper model.

Findings

The theory accurately predicts mobility edges in quasiperiodic models.

Results agree well with exact diagonalisation data.

The framework applies broadly to various quasiperiodic systems.

Abstract

We introduce a self-consistent theory of mobility edges in nearest-neighbour tight-binding chains with quasiperiodic potentials. Demarcating boundaries between localised and extended states in the space of system parameters and energy, mobility edges are generic in quasiperiodic systems which lack the energy-independent self-duality of the commonly studied Aubry-Andr\'e-Harper model. The potentials in such systems are strongly and infinite-range correlated, reflecting their deterministic nature and rendering the problem distinct from that of disordered systems. Importantly, the underlying theoretical framework introduced is model-independent, thus allowing analytical extraction of mobility edge trajectories for arbitrary quasiperiodic systems. We exemplify the theory using two families of models, and show the results to be in very good agreement with the exactly known mobility edges as well numerical results obtained from exact diagonalisation.