  We study a thermal and a transverse magnetic field response of a vortex line
array confined to a plane with a single columnar pinning defect. By integrating
out ``bulk'' degrees of freedom away from the columnar defect we reduce this
two-dimensional problem to a one-dimensional one, localized on the defect and
exhibiting a long-range elasticity along the defect. We show that as a function
of temperature, for a magnetic field aligned with the defect this system
exhibits a one-dimensional analog of a roughening transition, with a
low-temperature ``smooth'' phase corresponding to a vortex array pinned by the
defect, and a high-temperature ``rough'' phase in which at long scales thermal
fluctuations effectively average away the pinning by the defect. We also find
that in the low-temperature pinned phase, the vortex lattice tilt response to a
transverse magnetic field proceeds via a soliton proliferation transition,
governed by an integrable sine-Hilbert equation and analogous to the well-known
commensurate-incommensurate transition in sine-Gordon systems. The
distinguishing feature here is the long-range nature of the one-dimensional
elasticity, leading to a logarithmic soliton energy and interaction. We predict
the transverse-field -- temperature phase diagram and discuss extension of our
results to a bulk vortex array in the presence of a distribution of columnar
defects.
