Entanglement Spectrum as a Probe for the Topology of a Spin-Orbit Coupled Superconductor

Abstract: The classification of electron systems according to their topology has been at the forefront of condensed matter research in recent years. It has been found that systems of the same symmetry, previously thought of as equivalent, may in fact be distinguished by their topological properties. Moreover, the non-trivial topology found in some insulators and superconductors has profound physical implications that can be observed experimentally and can potentially be used for applications. However, characterizing a system's topology is not always a simple task, even for a theoretical model. When translation and other symmetries are present in a quadratic model the topological invariants are readily defined and easily calculated in a variety of symmetry classes. However, once interactions or disorder come into play the task becomes difficult, and in many cases prohibitively so. The goal of this paper is to suggest alternatives to the topological invariants which are based on the entanglement spectrum and entanglement entropy. Using quadratic models of superconductors we demonstrate that these entanglement properties are sensitive to changes in topology. We choose quadratic models since the topological phase diagram can be mapped using the topological invariants and then compared to the entanglement entropy/spectrum features. This work sets the stage for learning about topology in interacting and disordered systems through their entanglement properties.