Comment on "Metal-Insulator Transition in an Aperiodic Ladder Network: An Exact Result"

TL;DR

This paper critiques prior claims of multiple mobility edges in an aperiodic ladder network, showing that the model reduces to two non-interacting chains with separate critical points, and clarifies the conditions for true mobility edges.

Contribution

It clarifies the spectral properties of the aperiodic ladder model, demonstrating that the claimed mobility edges are artifacts of a basis change and not genuine transitions.

Findings

The model reduces to two decoupled chains with individual critical points.

Localized and delocalized states can coexist at the same energy without true mobility edges.

Analysis based solely on density of states and conductance can be misleading.

Abstract

Sil, Maiti, and Chakrabarti (SMC) (Phys. Rev. Lett. 101, 076803 (2008), arXiv:0801.2670) introduce an aperiodic two-leg ladder network composed of atomic sites with on-site potentials distributed according to a quasiperiodic Aubry-Andre potential. SMC claim the existence of multiple mobility edges, i.e. metal-insulator transitions at multiple values of the Fermi energy. SMC use numerical calculations of the conductance and den- sity of states, and an analytical result in a limiting case. In the following, we restate in the real space the change of basis done by SMC. This change of basis reduces their model to two decoupled chains, each with its own Aubry- Andre potential. Each of the chains has its own critical point, where all states change from metallic to insulat- ing, without any notion of a mobility edge. Since the two chains are not interacting, their spectra may overlap such that localized states (from one chain) and delocal- ized states (from the other chain) coexist at the same en- ergy. Consequently, the analysis of the density of states and the conductance alone is misleading, and that is due to the choice of the symmetric quasiperiodic potential. We briefly outline the possibility to obtain true mobility edges.