  In periodic systems of interacting electrons, Fermi and Luttinger surfaces
refer to the locations within the Brillouin zone of poles and zeros,
respectively, of the single-particle Green's function at zero energy and
temperature. Such difference in analytic properties underlies the emergence of
well-defined quasiparticles close to a Fermi surface, in contrast to their
supposed non-existence close to a Luttinger surface, where the single-particle
density-of-states vanishes at zero energy. We here show that, contrary to such
common belief, coherent `quasiparticles' do exist also approaching a Luttinger
surface in compressible interacting electron systems. Thermodynamic and dynamic
properties of such 'quasiparticles' are just those of conventional ones. For
instance, they yield well defined quantum oscillations in Luttinger's surface
and linear in temperature specific heat, which is striking given the vanishing
density of states of physical electrons, but actually not uncommon in strongly
correlated materials.
