Bipartite charge fluctuations in Z_2 topological insulators and superconductors (Dr. L. Herviou)

In this seminar, we study the BCF in generic one- and two-dimensional $\mathbb{Z}_2$ (topological) models such as the Kitaev chain, spin-orbit insulators, the graphene and the Haldane model, where the charge we observe is no longer conserved. In one-dimension, we demonstrate that at phase transitions characterized by a linear dispersion, the BCF probe the change in a winding number that allows to pinpoint the transition and corresponds to the topological invariant for standard models.

Additionally, we prove that a sub-dominant logarithmic contribution is still present at the exact critical point. Its quantized coefficient is universal and a characteristic of the critical model. In two dimensions, a similar structure appears. While the area term no longer reveal directly the phase transition, a subdominant logarithmic term is still present. Similarly to the entanglement entropy, it depends on the exact shape of the considered region, with contributions of the corner of the regions only.