In my understanding, quasi-particles were just some real world particle (like electrons) but in different environment i.e. an electron in a crystal.
Recently, I have started studying Spintronics/Magnetism and I see words like "quasi-particle", "excitations" and "elementary excitation" a lot. For example Spinons, anyons, magnons etc. And they are very confusing for me. I can't imagine how these particles form.
On many places I see that researchers write "The elementary excitation of this/that state/wave is a spinon/anyon/magnon." How can a wave give an excitation particle?
After reading all this I feel like quasi-particles are not real particles but just some mathematical tools to solve a system/Hamiltonian. Am I right?
In short, what are quasi-particles/elementary excitations? How can a beginner imagine/make picture of these concepts for better understanding?