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It is expected that the interplay between non-trivial band topology andstrong electron correlation will lead to very rich physics. Thus a controlledstudy of the competition between topology and correlation is of great interest.Here, employing large-scale quantum Monte Carlo (QMC) simulations, we provide aconcrete example of the Kane-Mele-Hubbard (KMH) model on an AA stacking bilayerhoneycomb lattice with inter-layer antiferromagnetic interaction. Oursimulation identified several different phases: a quantum spin-Hall insulator(QSH), a $xy$-plane antiferromagnetic Mott insulator ($xy$-AFM) and aninter-layer dimer-singlet insulator (dimer-singlet). Most importantly, a bonafide topological phase transition between the QSH and the dimer-singletinsulators, purely driven by the inter-layer antiferromagnetic interaction isfound. At the transition, the spin and charge gap of the system close while thesingle-particle excitations remain gapped, which means that this transition hasno mean field analogue and it can be viewed as a transition between bosonic SPTstates. At one special point, this transition is described by a $(2+1)d$ $O(4)$nonlinear sigma model (NLSM) with {\it exact} $SO(4)$ symmetry, and atopological term at {\it exactly} $\Theta = \pi$. Relevance of this worktowards more general interacting SPT states is discussed.

Bona fide interaction-driven topological phase transition in correlated SPT states