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The Z2 topological invariant, spin Chern number and zero-frequency Green's functions in correlated topological insulators

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The stability of
topological insulators under electronic correlation has been an elusive yet
central topic. In this talk, we will discuss the correlation effects in the two
descendants of the Kane-Mele-Hubbard model, called generalized
Kane-Mele-Hubbard model and dimerized Kane-Mele-Hubbard model, by means of the
sign-free Quantum Monte Carlo (QMC) method. In the non-interacting limit, both
systems undergo topological phase transitions by tuning tight-binding (one-body)
parameters. Under interaction, we can compute the topological invariant, the Z2
invariant and spin Chern number,and observe the zero-frequency Green's function
behavior to identify the phase transition in finite-size clusters with the QMC. We found that the quantum fluctuations from interaction may either stabilize or
destabilize the topological insulator phase in the KMH models, depending on the
symmetry character of the one-body parameter. Our numerical results suggest
that as the one-body term preserves the lattice symmetry,correlation stabilizes
the topological insulators whereas destabilizes.