Entanglement as a topological marker in harmonically confined attractive Fermi–Hubbard chains

Abstract

We investigate the single-site von Neumann entropy along a harmonically confined superfluid chain, as described by the one-dimensional fermionic Hubbard model with strongly attractive interactions. We find that by increasing the confinement (or equivalently the particle filling), the system undergoes a quantum phase transition from a superfluid (SF) to a non-trivial topological insulator (TI) phase, which is characterized by an insulating bulk surrounded by highly entangled superfluid edges. These highly entangled states are found to be robust against perturbations and topologically protected by the particle–hole symmetry, which is locally preserved. We also find a semi-quantitative agreement between entanglement and superconducting order parameter profiles, confirming that entanglement can be used as a topological marker and an order parameter in these systems. The charge gap not only confirms the SF–TI transition but also shows that this transition is mediated by a metallic intermediate regime within the bulk. Using the gap, we could depict a phase diagram for which the non-trivial topological insulator can be found in such harmonically confined attractive systems.