Non-Hermitian Luttinger Liquids and Vortex Physics

As a model of two thermally excited flux liquids connected by a weak link, we study the effect of a single line defect on vortex filaments oriented parallel to the surface of a thin planar superconductor. When the applied field is tilted relative to the line defect, the physics is described by a nonhermitian Luttinger liquid of interacting quantum bosons in one spatial dimension with a point defect. We analyze this problem using a combination of analytic and numerical density matrix renormalization group methods, uncovering a delicate interplay between enhancement of pinning due to Luttinger liquid effects and depinning due to the tilted magnetic field. Interactions dramatically improve the ability of a single columnar pin to suppress vortex tilt when the Luttinger liquid parameter g is less than or equal to one.