  Distinguishing the nontrivial symmetry-protected topological (SPT) phase from
the trivial insulator phase in the presence of electron-electron interaction is
an urgent question to the study of topological insulators, due to the fact that
most of the topological indices defined for free electron systems are very
likely unsuitable for interacting cases. In this work, we demonstrate that the
strange correlator is a sensitive diagnosis to detect SPT states in interacting
systems. Employing large-scale quantum Monte Carlo (QMC) simulations, we
investigate the interaction-driven quantum phase transition in the
Kane-Mele-Hubbard model. The transition from the quantum spin Hall insulator at
weak interaction to an antiferromagnetic Mott insulator at strong interaction
can be readily detected by the momentum space behavior of the strange
correlator in single-particle, spin, and pairing sectors. The interaction
effects on the symmetry-protected edge states in various sectors, i.e., the
helical Luttinger liquid behavior, are well captured in the QMC measurements of
strange correlators. Moreover, we demonstrate that the strange correlator is
technically easier to implement in QMC and more robust in performance than
other proposed numerical diagnoses for interacting topological states, as only
static correlations are needed. The attempt in this work paves the way for
using the strange correlator to study interaction-driven topological phase
transitions in fermionic as well as bosonic systems.
