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Is a phonon a quasiparticle or a collective excitation?
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It is both. ''quasiparticle'' is the formal notion (defined via an 
appropriate Bogolubov transformation), while ''collective excitation'' 
is the intuitive version of what the notion should convey.

Note that solid-state physics is quantum fiels theory, so even 
(quasi)''particles'' are described by fields. The particleness only 
refers to the fact that they are describe by the same framework 
involving creation and annihilation operators as elelemtary particles.