  Interaction-driven topological phase transitions in Dirac semimetals are
investigated by means of large-scale quantum Monte Carlo (QMC) simulations. The
interaction among Dirac fermions is introduced by coupling them to Ising spins
that realize the quantum dynamics of the two-dimensional transverse field Ising
model. The ground state phase diagram, in which the tuning parameters are the
transverse field and the coupling between fermion and Ising spins, is
determined. At weak and intermediate coupling, a second-order Ising quantum
phase transition and a first-order topological phase transition between two
topologically distinct Dirac semimetals are observed. Interestingly, at the
latter, the Dirac points smear out to form nodal lines in the Brillouin zone,
and collective bosonic fluctuations with SO(4) symmetry are strongly enhanced.
At strong coupling, these two phase boundaries merge into a first-order
transition.
