Isolated extended states and anomalous critical behavior in the generalized SSH model

TL;DR

This paper explores how extended states and multifractal phases emerge and transition in a generalized SSH model, revealing novel critical behaviors and the influence of band edge states.

Contribution

It uncovers the protection of extended states by unbounded hopping and their transition to multifractal phases due to incommensurate zeros, providing new insights into localization phenomena.

Findings

Extended states are protected by unbounded hopping.

Transition from extended to multifractal phase occurs via incommensurate zeros.

Extended states originate from SSH model band edges and affect critical transitions.

Abstract

We investigate the localization properties of a generalized SSH model. Numerical and analytical results indicate the emergence of extended states protected by unbounded hopping in this model. Moreover, this protection effect is disrupted by the appearance of generalized incommensurate zeros, causing the extended phase in the system to transition into a multifractal phase. However, at the boundaries of the phase region, we still observe the existence of extended states. These extended states coincide with multifractality-enriched mobility edges, separating the multifractal phase from the localized phase. Further analysis reveals that this extended states originates from the band edge states of SSH model. In addition, these isolated extended states also influence eigenstates with nearby energies, giving rise to an anomalous extended-to-multifractal critical transition. These findings not only enrich the behavioral repertoire of eigenstates at critical points, but also offer new insights for further understanding Anderson localization and the induction of multifractal phases.