Abstract: The concept of quasiparticle or elementary excitations can be used to describe the physical properties of a macroscopic object in a low-excited state. Different physical models correspond to different quasiparticles, and these quasiparticles make the complicated multi-body problem easier to deal with. In three or more than three-dimensional space, according to the spin properties of particles, particles with half-integer and integer spin are consistent with Fermi-Dirac statistics and Bose-Einstein statistics, respectively. In 1977, after studying the topological properties of two-dimensional space by Leinaas and Myrheim, a kind of quasiparticle-anyon with the fractional statistics is proposed. With the development of two-dimensional physical systems, anyon has changed from pure theoretical research to practical research object.

Key words: quasiparticles, elementary excitation, anyon, statistical laws