  We study the phase structure and charge transport at finite temperature and
chemical potential in the non-Hermitian PT-symmetric holographic model of
arXiv:1912.06647. The non-Hermitian PT-symmetric deformation is realized by
promoting the parameter of a global U(1) symmetry to a complex number.
Depending on the strength of the deformation, we find three phases: stable
PT-symmetric phase, unstable PT-symmetric phase, and an unstable PT-symmetry
broken phase. In the three phases, the square of the condensate and also the
spectral weight of the AC conductivity at zero frequency are, respectively,
positive, negative, and complex. We check that the Ferrell-Glover-Tinkham sum
rule for the AC conductivity holds in all the three phases. We also investigate
a complexified U(1) rotor model with PT-symmetric deformation, derive its phase
structure and condensation pattern, and find a zero frequency spectral weight
analogous to the holographic model.
