Interaction effects in non-Hermitian models of vortex physics

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.