  A characteristic feature of Shiba impurities is the existence of a spin- and
parity-changing quantum phase transition (known as "0-$\pi$" transition) which
has been observed in scanning tunneling microscopy (STM) and transport
experiments. Using the Abelian bosonization technique, here we analyze the
ground-state properties and the quantum phase diagram of a classical (i.e.,
Ising-like) Shiba impurity. In particular, we analyze the cases of an impurity
in a three- and a one-dimensional superconductor. Within the bosonization
framework, the ground-state properties are determined by simple soliton-like
solutions of the classical equations of motion of the bosonic fields, whose
topological charge is related to the spin and parity quantum numbers. Our
results indicate that the quantum phase diagram of the superconductor can be
strongly affected by geometrical and dimensional effects. Exploiting this fact,
in the one-dimensional case we propose an experimental superconducting
nanodevice in which a novel parity-preserving, spin-changing "0-0" transition
is predicted.
