Do we know exactly the difference between particles and quasiparticles? Is Higgs boson a particle or a quasiparticle? I ask this because if I understood well, Higgs boson created by a spontaneaous breaking symmetry and correspond to a Goldstone mode. Maybe I am wrong in my explication.
A quasiparticle is an elementary collective nonlocal excitation of a quantum medium (such as a crystal); examples are phonons (describing sound waves) or Cooper pairs (describing superconductivity). In contrast, a particle is (in the context of high energy physics) the elementary excitation of a local quantum field; examples are the electron or the photon.
In the standard model, the Higgs is modelled as a local field, hence is a particle, but there are alternative scenarios, where the Higgs is not built into the theory as a field but emerges as a collective excitation and hence is a quasipartice. To distinguish between these scenarios requires experimental input that doesn't yet exist.
A quasiparticle is a particle-like entity with definite internal structure and size. Quantization rules make such structures more "real" and more strongly conserved than than similar classical constructs would be.
In semiconductors, the entity known as a hole is a good example of a quasiparticle. It behaves very much like a particle carrying positive charge, although in reality it's just an absence of an electron. Holes unavoidably involved many particles to exist, including the atoms of the semiconductor lattice and its electrons.
A notable feature of a quasiparticle is that since it is constructed out of more fundamental particles, they always have definite and non-zero sizes in space. They can never be modeled as true points, as can for example an electron.
The Higgs boson in contrast is proposed to be a fundamental particle that does not require any other particles to exist. It thus is very definitely not a quasiparticle, but is instead a fundamental particle in the same "no visible internal structure" sense of a photon or electron.
The reason all of this can get a bit confusing is that because quasiparticles reflect fundamental quantization and conservation laws, they are in many cases subject to many of the same mechanisms seen for more fundamental particles. That's why you see Nambu–Goldstone bosons invoked in both fundamental physics and in solid state physics. It is a reflection of the generality of the Nambu–Goldstone mechanism, rather than an assertion about the presence or absence of lower-level structure in the particles that are involved.
Pair creation is another example of a rule that applies across both fundamental particles and quasiparticles.
Pair creation is the mechanism by which a sufficiently energetic gamma ray can be converted into a free-space electron and a free-space positron. That process exists fully within fundamental physics, since the gamma photon, electron, and positron all show no evidence of deeper structure at available energy levels.
However, a curiously parallel pair creation process also occurs at much lower energy levels when a photon strikes the right kind of semiconductor lattice. That lower-energy photon also creates a pair of charged quasiparticles and creates. One is a conduction electron, which within a semiconductor involves the local atomic lattice through which so it moves. It is thus best modeled as a quasiparticle that has both structure and size, one that happens to include an electron to give it charge. The other quasiparticle is a hole, which similarly involves the lattice and has no fundamental particle at all behind its version of positive charge.
Similarly, the Nambu–Goldstone mechanism can apply both all-fundamental particle sets, or to all-quasiparticle (or mixed) particle sets.