  A unified theory of quantum critical points beyond the conventional
Landau-Ginzburg-Wilson paradigm remains unknown. According to Landau cubic
criterion, phase transitions should be first-order when cubic terms of order
parameters are allowed by symmetry in the Landau-Ginzburg free energy. Here,
from renormalization group (RG) analysis we show that second-order quantum
phase transitions can occur at such putatively first-order transitions in
interacting two-dimensional Dirac semimetals. As such type of Landau-forbidden
quantum critical points are induced by gapless fermions, we call them
fermion-induced quantum critical points (FIQCP). We further introduce a
microscopic model of SU(N) fermions on the honeycomb lattice featuring a
transition between Dirac semimetals and Kekule valence bond solids. Remarkably,
our large-scale sign-problem-free Majorana quantum Monte Carlo simulations show
convincing evidences of a FIQCP for N=2,3,4,5,6, consistent with the RG
analysis. We finally discuss possible experimental realizations of the FIQCP in
graphene and graphene-like materials.
