| Abstract [eng] |
The discovery of fractional quantum Hall effect (FQHE) in 2D electron gas gave rise to immense interest in topological phases of matter. One of the most intriguing features of FQHE state is fractionally charged excitations which embodies anyonic statistics. Even though the FQHE was first observed in GaAs-GaAlAs heterojunctions, experiments in optical lattices allow much more controllable study of many-body systems, therefore allowing regimes that are impossible to realise in semiconductor based experiments. Historically, FQHE comes from condensed matter systems, which can be characterized by a very large number of particles, as a consequence, theoretical studies were focused only on infinite or periodical Hamiltonians. Therefore, few of the unanswered questions remain: can FQHE states be realised in minuscule lattices, containing only several sites in diameter, and what additional effects would open boundaries produce? In this work we try to tackle both of these questions. Using numerical diagonalization of Harper-Hofstadter model we were able to observe localisation of fractional charge in a 9×6 square lattice with artificial magnetic flux. Unfortunately, close proximity to the lattice edges does not allow direct confirmation of fractional statistics. |
