It's not clear to me what are the elementary excitations of Luttinger liquids. Quoting from Giamarchi's book Quantum Physics in One Dimension:
In one dimension, [...], an electron that tries to propagate has to push its neighbours because of electron-electron interactions. No individual motion in possible. Any individual excitation has to become a collective one.
Judging by this, I would say that in Luttinger liquids the elementary excitations can only be a collective one, regarding the system as a whole. But then, talking about the bosonization method for solving such systems, it is said:
It means that in one dimension the particle-hole excitations are well-defined "particles" [...]. These bosonic quasiparticles will just be the key in solving our one-dimensional problem.
Along these lines is this quote from Sénéchal's notes An introduction to bosonization:
The basic idea behind bosonization is that particle-hole excitations are bosonic in character, and that somewhat the greatest part (if not the totality) of the electron gas spectrum might be exhausted by these excitations.
And judging by this I would say that particle-hole excitations, which are bosonic in nature, are the elementary excitations of the system.
What is, exactly, going on physically in a Luttinger liquid?