Theoretical models towards experimental realization of anyons

Abstract

Za razliku od trodimenzionalnog prostora u kojem mogu egzistirati samo fermioni i bozoni, u dvodimenzionalnom svijetu možemo imati kvazičestice koje zadovoljavaju drugačiju statistiku. Prilikom zamjene dvije identične kvazičestice, valna funkcija dobiva fazni faktor eiπα gdje je α realni broj između 0 i 1. Stoga one nisu niti fermioni niti bozoni, već ih nazivamo anyonima. U ovom radu uveli smo pojam anyona preko jednostavnog primjera cilindara s tokom magnetskog polja Φ i česticom naboja q. To je najjednostavniji primjer anyona i njega je razmatrao Wilczek [5]. Jedini poznati efekt u prirodi koji pokazuje anyonska pobuđenja je kvantni Hallov efekt. Ostalih eksperimentalnih realizacija nema. Današnja istraživanja su usmjerena na mnogočestične sustave sa anyonskim pobuđenjima. Ovaj rad je različit od takvih pristupa jer su promatrane samo dvije čestice na koje smo nametnuli interakciju koja daje topološku fazu nakon zamjene čestica. Prva razmatrana interakcija je obična dipol-dipol za koju smo pokazali da ne daje topološku fazu. Njenom modifikacijom, izbacujući ovisnost o udaljenosti čestica iz interakcije, dobili smo topološku fazu nakon zamjene čestica, odnosno anyone. Pokazali smo da anyoni dobiveni takvom interakcijom nisu slobodni, već interagiraju potencijalom ovisnim o vanjskom magnetskom polju B i udaljenosti između čestica.In three-dimensional space we can find only two types of particles regarding their statistics, fermions and bosons. When we restrict the system to two dimensions, different statistics can be obtained which is not necessarily purely fermionic or bosonic. Particles obeying that statistics are called anyons. Exchanging two identical anyons, wave function gets a phase factor eiπα where α can be any real number between 0 and 1. First we discuss the simplest model of anyons, originally discussed by Wilczek [5], where anyons are flux-tubes with magnetic flux Φ and charge q. The only known example of anyonic excitations in nature is fractional quantum Hall effect and no other experimental realization of anyons is achieved up to this date. Most of research is based on many-body systems with anyonic excitations, while this work has a different approach. We were using only two spin particles with imposed interaction to get topological phase after exchanging two identical particles. First interaction we considered was dipol-dipol interaction, not showing s topological phase. Modifying interaction by neglecting the dependency on distance between particles, we observed the topological phase. Anyons emerging from modified model are not free but interact via a potential which depends on external magnetic field B and the distance between anyons