  In the vicinity of the quantum critical point(QCP), thermodynamic properties
diverge toward zero temperature governed by universal exponents. Although this
fact is well known, how it is reflected in quantum dynamics has not been
addressed. As an ideal experimental platform to test the issue, we consider an
organic Mott insulator whose dielectric degrees of freedom, a quantum electric
dipole, is described by the transverse Ising model on a triangular lattice that
has a QCP. We track the Glauber-type dynamics of the model by constructing a
kinetic protocol based on the quantum Monte Carlo method. The dynamical
susceptibility takes the form of the Debye function and shows a significant
peak-narrowing in approaching a QCP due to the divergence of the relaxation
timescale. It resembles the anomaly of dielectric constants observed in the
organic materials \k{appa}-ET 2 X dimer Mott insulating phase, indicating that
the material is very near the ferroelectric QCP.
