  Quantum mechanical spreading of a particle hopping on tight binding lattices
can be suppressed by the application of an external ac force, leading to
periodic wave packet reconstruction. Such a phenomenon, referred to as dynamic
localization (DL), occurs for certain magic values of the ratio $\Gamma=F_0/
\omega$ between the amplitude $F_0$ and frequency $\omega$ of the ac force. It
is generally believed that in the low-frequency limit ($\omega \rightarrow 0$)
DL can be achieved for an infinitesimally small value of the force $F_0$, i.e.
at finite values of $\Gamma$. Such a normal behavior is found in homogeneous
lattices as well as in inhomogeneous lattices of Glauber-Fock type. Here we
introduce a tight-binding lattice model with inhomogeneous hopping rates,
referred to as pseudo Glauber-Fock lattice, which shows DL but fails to
reproduce the normal low-frequency behavior of homogeneous and Glauber-Fock
lattices. In pseudo Glauber-Fock lattices, DL can be exactly realized, however
at the DL condition the force amplitude $F_0$ remains finite as $\omega
\rightarrow 0$. Such an anomalous behavior is explained in terms of a
$\mathcal{PT}$ symmetry breaking transition of an associated two-level
non-Hermitian Hamiltonian that effectively describes the dynamics of the
Hermitian lattice model.
