A central problem in the theory of strongly correlated fermion systems, concerns the
nature of their low-lying excitations. It is generally accepted that, except for special
cases with symmetry breaking, three dimensional (3D) interacting Fermi systems, are well
described in terms of weakly correlated quasi-particles with quantum numbers in one-toone
correspondence with those identifying the excitations of a non-interacting Fermi gas.
This is the basic assumption underlying the Landau theory of Fermi liquids (FL), which
was originally proposed as a phenomenological description of strongly interacting fermions
by Landau in early 1956[1), an then established microscopically by Nozieres and Luttinger
in 1962[2].
Quite a different scenario occurs in lD interacting Fermi systems. Apart from specific
models developing gaps in the excitation spectrum, most fermion systems in one
dimension with repulsive interactions, do have low-lying gapless excitations, like ordinary
Fermi liquids, but totally different from the quasi-particles predicted by Landau theory.
The low-energy behavior of most of these lD interacting fermion systems with gapless
linear excitations, can be understood in terms of few model dependent constants, which
parametrize all the long-wavelength properties...
