Scaling of critical wavefunctions at topological Anderson transitions in 1D

TL;DR

This paper investigates the properties of critical wavefunctions at topological Anderson transitions in 1D, revealing inhomogeneous local moments with edge amplification and providing an analytic expression validated by simulations.

Contribution

It introduces an analytic expression for the spatial profile of local moments at 1D topological Anderson transitions, confirmed through numerical models.

Findings

Local moments are strongly inhomogeneous with edge amplification.

Analytic expression for the spatial profile of local moments.

Validation of the analytic model with numerical simulations.

Abstract

Topological Anderson transitions, which are direct phase transitions between topologically distinct Anderson localised phases, allow for criticality in 1D disordered systems. We analyse the statistical properties of an emsemble of critical wavefunctions at such transitions. We find that the local moments are strongly inhomogeneous, with significant amplification towards the edges of the system. In particular, we obtain an analytic expression for the spatial profile of the local moments which is valid at all topological Anderson transitions in 1D, as we verify by direct comparison with numerical simulations of various lattice models.