Anyon braiding in semi-analytical fractional quantum Hall lattice models

Abstract

It has been demonstrated numerically, mainly by considering ground state properties, that fractional quantum Hall physics can appear in lattice systems, but it is very difficult to study the anyons directly. Here, I propose to solve this problem by using conformal field theory to build semi-analytical fractional quantum Hall lattice models having anyons in their ground states, and I carry out the construction explicitly for the family of bosonic and fermionic Laughlin states. This enables me to show directly that the braiding properties of the anyons are those expected from analytical continuation of the wave functions and to compute properties such as internal structure, size, and charge of the anyons with simple Monte Carlo simulations. The models can also be used to study how the anyons behave when they approach or even pass through the edge of the sample. Finally, I compute the effective magnetic field seen by the anyons, which varies periodically due to the presence of the lattice.