Question

Significance of the correlation length in topological insuulatirsa ,

Answer 1

The correlation functions related to topological phase transitions in inversion-symmetric lattice models described by 2×2 Dirac Hamiltonians are discussed. In one dimension, the correlation function measures the charge-polarization correlation between Wannier states at different positions, while in two dimensions it measures the itinerant-circulation correlation between Wannier states. The correlation function is nonzero in both the topologically trivial and nontrivial states, and allows to extract a correlation length that diverges at topological phase transitions..