Many-body marker for three-dimensional topological insulators with inversion symmetry

We extend the previously defined many-body marker for two-dimensional Z2 topological insulators [I. Gilardoni et al., Phys. Rev. B 106, L161106 (2022)] to distinguish trivial, weak, and strong topological insulators in three dimensions, in the presence of inversion symmetry. The marker is written in terms of ground-state expectation values of position operators and can be employed to detect topological phases of interacting systems beyond mean-field approximations, e.g., within quantum Monte Carlo techniques. Here we show that the correct results of the noninteracting limit are reproduced by the many-body marker.