  We show that classical DNA unzipping transition which is equivalently
described by quantum mechanical localization-delocalization transition in the
ground state of non-Hermitian Hatano-Nelson Hamiltonian is underpinned by
generalized parity (P)-time reversal (T) symmetry breaking transition. We also
study the one-dimensional discretized version of Hatano-Nelson model in the
presence of the single impurity and quasiperiodic potential on a finite-size
lattice. Our results show that these models undergo a phase transition from a
PT unbroken phase to a broken phase. Interestingly, the generalized PT phase
transition points also coincide with the localization-delocalization transition
for both models.
