  Dark photon dark matter may be produced by the cosmic strings in association
with the dark U(1) gauge symmetry breaking. We perform three-dimensional
lattice simulations of the Abelian-Higgs model and follow the evolution of
cosmic strings. In particular, we simulate the case of (very) light vector
boson and find that such vector bosons are efficiently produced by the collapse
of small loops while the production is inefficient in the case of heavy vector
boson. We calculate the spectrum of the gravitational wave background produced
by the cosmic string loops for the light vector boson case and find
characteristic features in the spectrum, which can serve as a probe of the dark
photon dark matter scenario. In particular, we find that the current
ground-based detectors may be sensitive to such gravitational wave signals and
also on-going/future pulsar timing observations give stringent constraint on
the dark photon dark matter scenario.
