Vortex pinning and the non-Hermitian Mott transition

The boson Hubbard model has been extensively studied as a model of the zero temperature superfluid/insulator transition in ⁴He 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 Hc1, with the additional feature that the direction of the tilted vortices at the transition bears a nontrivial relationship to the direction of the applied magnetic field. The properties of the Mott insulator and flux liquid phases with tilt are also discussed.