  The Dirac-like electronic structure can host a large number of competing
orders in the form of mass terms. In particular, two different order parameters
can be said to be dual to each other, when a static defect in one of them traps
a quantum number (or "charge") of the other. We discuss that such complementary
nature of the pair of the order parameters shows up in their correlation
functions and dynamical properties when a quantum phase transition is driven by
fluctuations of the one of the order parameters. Approaching the transition
from the disordered (paramagnetic) side, the order parameter correlation
function at the critical point is reduced, while such fluctuations enhance the
correlation of the dual order parameter. Such complementary behaviors in the
correlation function can be used to diagnose the nature of quantum fluctuations
that is the driving force of the quantum phase transition.
