We employ large-scale quantum Monte Carlo simulations, i.e., determinantal QMC and continuous time QMC for interacting fermion systems, to pursue the understanding of interaction effects on topological state of matter, such as the validity of topological index in the interaction-driven topological phase transitions (__Phys. Rev. B 93, 195163 (2016)__, __Phys. Rev. B 93, 195164 (2016)__), the emergent bosonic symmetry protected topological phase in an interacting fermion model (__arXiv:1606.05822__, also see the figure above), and the novel bulk phase transition associated with topological term in the quantum field theory description (__Phys. Rev. B 93, 115150 (2016)__, __arXiv:1606.05822__). Moreover, the deep connection between the interaction effect in topological state of matter in condensed matter systems and the emergent of chiral fermions in the standard model in high-energy phase, is also a question we'd like to reveal via our numerical investigations (__arXiv:1603.08376__).

We employ large-scale quantum Monte Carlo simulations, i.e., stochastic series expansion and worm-algorithm in the path-integral framework, to pursue the understanding of quantum phase transition and novel quantum phases in the (frustrated) quantum magnetic systems, such as the logarithmic corrections and amplitude (Higgs) mode in the (3+1) D O(3) antiferromagnet to dimer-singlet quantum phase transition (__Phys. Rev. B 92, 214401 (2015)__, also see the figure above), the Coulomb U(1) quantum spin liquid phase in the frustrated XXZ model on the pyrochlore lattice (__Phys. Rev. Lett. 115, 037202 (2015)__), the Z2 quantmum spin liquid phase in the frustrated XXZ model on the kagome lattice. Moreover, the dynamic spectrum information close to the magnetic quantum critical point, are also being actively explored by our state-of-art QMC+analytical continuation approaches.

We are developing new quantum Monte Carlo scheme, that incorporate the critical bosonic fluctuations to Fermi surface or Fermi point in an unbiased manner, such that the long-standing problem of the metallic quantum critical point can be addressed without approximation. Our attempt in anisotropic velocity fluctuations of Dirac fermions (__arXiv:1602.07150__, and see the figure above) has revealed rich phase diagram that contains topological phase transition and enhanced SO(4) fermion bilinear fluctuations in the dynamically degenerated nodal lines. Investigations of bosonic flucutations on a full Fermi surface are on-going.