# Rigorous distinction between quasiparticles and collective excitations

I would like to hear your opinion on the question whether there is an accepted distinction between both concepts in condensed matter physics. I would tend to use the word quasiparticle for dressed fermionic particles and the term collective excitation in the case of bosonic excitation. But considering for example magnons in ferromagnets makes it very arbitrary kind of definition since magnons can be viewed (if I am not wrong) both as quasiparticles and also as collective excitations.

• In nuclear physics, we have collective excitations such as rotations and vibrations, and quasiparticle excitations of the nucleons. There is no clean distinction between the two. For example, one can have a chain of even-even nuclei with neutron and proton numbers $(N,Z)$, $(N,Z+2)$, $(N,Z+4)$, ... such that one end of the chain demonstrates nearly pure quasiparticle excitations, while the other end is a deformed rotor with highly collective excited states. The ones in between interpolate between these two extremes. – Ben Crowell Sep 12 '14 at 15:45

## 2 Answers

I've tracked a variety of quasiparticle issues for over 20 years now, including a couple of deep literature dives on fractionally charged topological solitons in materials such as polyacetylene. The term quasiparticle has always dominated in the articles I've found. That's true even for integer spin excitations, which after all are quite particle-like in their quantum behaviors, despite lacking a more fundamental particle such as an electron in their cores. So when I've occasionally seen the phrase "collective excitation," I never thought to interpret as anything more than a more detailed way of describing what a quasiparticle is. Thus the phrase to me has no overt connotation of why it should be attached only to integer spin quasiparticles. Finally, I note that Wikipedia seems to have captured a similar sentiment in its page on quasiparticles.

A highly subjective answer:

I've always imagined "collective excitation" more as a subset under "quasiparticle" than as an alternative. The classification I usually do is that a quasiparticle is either a "dressed state" or a "collective excitation." The difference between the two is that a dressed state is adiabatically connected to some particle in a non-interacting limit, while a collective excitation is not. The fact that one term is more often used for fermions and the other for bosons is basically a coincidence to my mind, and comes from the fact that the favorite example of each type of quasiparticle (Landau liquid electrons and phonons, respectively) happen to be canonical examples of the two alternatives.

Certainly, things are not always this cut and dried- in addition to smooth crossovers of the kind that Ben Crowell mentions, one could imagine, say, a superfluid with phonon excitations that are themselves dressed by interaction with some other system. In this case, one could presumably refer to these excitations as dressed collective excitation quasiparticles, although that would be a bit of a mouthful. Choosing one of these terms over the other would emphasize a particular aspect of the excitation.

• A subjective answer to a subjective question. – DanielSank Apr 9 '15 at 4:05