Local Topological Markers for Disordered, Interacting, and Mixed States

Julia Hannukainen develops real-space topological diagnostics for disordered, interacting and mixed quantum states. In odd dimensions, gauge-dependent winding and Z2 forms obstruct a direct Fourier-space analogue of the Chern marker. Dimensional reduction overcomes this by expressing an even-dimensional Chern character through odd-dimensional data. The resulting local markers identify topology in amorphous three-dimensional insulators and superconductors, interacting Ising–Majorana states and Gaussian mixed states with a purity gap, extending diagnosis to finite-temperature and open-system settings.