Describing Quantum Entanglement in Topological Phases

Topological phases of insulators and superconductors constitute an interesting platform to realize entangled quantum states. We offer a constructive approach to relate quantum entanglement to topological features, respectively described by the Wootters concurrence and Berry connection. A precise relation between these two physical properties is proposed for two distinguishable qubits. We show that this simple system is describable in the framework of the tenfold classification of topological phases. The Chern number predicted for this zero dimensional and time reversal symmetric system is related to the Hopf fibration of the associated Hilbert space. Additional examples are given where time reversal invariance is broken.