The boson Hubbard model has been extensively studied as a model of the zero
temperature superfluid/insulator transition in Helium-4 on periodic substrates.
It can also serve as a model for vortex lines in superconductors with a
magnetic field parallel to a periodic array of columnar pins, due to a formal
analogy between the vortex lines and the statistical mechanics of quantum
bosons. When the magnetic field has a component perpendicular to the pins, this
analogy yields a non-Hermitian boson Hubbard model. At integer filling, we find
that for small transverse fields, the insulating phase is preserved, and the
transverse field is exponentially screened away from the boundaries of the
superconductor. At larger transverse fields, a ``superfluid'' phase of tilted,
entangled vortices appears. The universality class of the transition is found
to be that of vortex lines entering the Meissner phase at H_{c1}, with the
additional feature that the direction of the tilted vortices at the transition
bears a non-trivial relationship to the direction of the applied magnetic
field. The properties of the Mott Insulator and flux liquid phases with tilt
are also discussed.Comment: 20 pages, 12 figures included in text; to appear in Physical Review