Correlation Functions in Topological Chains

Abstract

Topological Insulators and superconductors have been studied intensively over the last decade and their topological phase transitions have been characterized by the change in the topological invariant. Recently, an approach that makes use of thermodynamics to describe the topological phase transitions has been proposed. In this approach, one can treat the bulk and the boundary contributions of the grand potential separately. We derived these contributions from the correlation functions and found perfect agreement with previous findings for the Kitaev chain. Subsequently, we applied the method to the 1D Weyl superconductor and the long-range Kitaev chain and showed that we can distinguish all the different phases in the 1DWeyl superconductor, without making use of a topological invariant. For the long range Kitaev chain, our results indicate a topological quantum critical point in the phase diagram. The correlation-function method turns out to be very efficient in terms of computational time, when compared to other approaches that provide equivalent results.