Non-Hermitian Luttinger liquids and flux line pinning in planar   superconductors
  As a model of 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. This problem can be mapped onto the physics of a Luttinger liquid of interacting bosons in 1 spatial dimension with a point impurity. When the applied magnetic field is tilted relative to the line defect, the corresponding quantum boson Hamiltonian is non-Hermitian. 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 allow a single columnar defect to be very effective in suppressing vortex tilt when the Luttinger liquid parameter g less than equal to 1. 
Ian Affleck, Walter Hofstetter, David R. Nelson and Ulrich Schollwock