  We study the properties of a D6-brane probe in the ABJM background with
smeared massless dynamical quarks in the Veneziano limit. Working at zero
temperature and non-vanishing charge density, we show that the system undergoes
a quantum phase transition in which the topology of the brane embedding changes
from a black hole to a Minkowski embedding. In the unflavored background the
phase transition is of second order and takes place when the charge density
vanishes. We determine the corresponding critical exponents and show that the
scaling behavior near the quantum critical point has multiplicative logarithmic
corrections. In the background with dynamical quarks the phase transition is of
first order and occurs at non-zero charge density. In this case we compute the
discontinuity of several physical quantities as functions of the number $N_f$
of unquenched quarks of the background.
