Topological insulators are physically distinguishable from normal insulators only near edges and defects, while in the bulk there is no clear signature to their topological order. In this work we show that the ${\mathbb{Z}}_2$ index of topological insulators and the $\mathbb{Z}$ index of the integer quantum Hall effect manifest themselves locally. We do so by providing an algorithm for determining these indices from a local equal time ground-state correlation function at any convenient boundary conditions. Our procedure is unaffected by the presence of disorder and can be naturally generalized to include weak interactions. The locality of these topological indices implies bulk-edge correspondence theorem.

• Received 26 May 2011

DOI:https://doi.org/10.1103/PhysRevB.83.245115