Universal Multifractality at the Topological Anderson Insulator Transition

Disorder is ubiquitous in quantum materials, and its interplay with topology can generate phases absent in the clean limit. Using the Haldane model as a minimal setting, we show that disorder not only shifts topological boundaries but also stabilizes a topological Anderson insulator (TAI) between trivial and Chern insulating regimes. Employing the local Chern marker as a real-space topological probe, we map the full phase diagram and demonstrate that the TAI forms a finite domain bounded by trivial and Anderson insulators. Multifractal analysis of low-energy eigenstates at the boundary reveals universal critical spectra, independent of whether disorder generates or destroys topology. These results place topology, localization, and criticality within a unified framework and provide clear benchmarks for real-space diagnostics of disordered topological phases.