  Vortex lines in superconductors in an external magnetic field slightly tilted
from randomly-distributed parallel columnar defects can be modeled by a system
of interacting bosons in a non-Hermitian vector potential and a random scalar
potential. We develop a theory of the strongly-disordered non-Hermitian boson
Hubbard model using the Hartree-Bogoliubov approximation and apply it to
calculate the complex energy spectra, the vortex tilt angle and the tilt
modulus of (1+1)-dimensional directed flux line systems. We construct the phase
diagram associated with the flux-liquid to Bose-glass transition and find that,
close to the phase boundary, the tilted flux liquid phase is characterized by a
band of localized excitations, with two mobility edges in its low-energy
spectrum.
