• anyons
• exact diagonalization
• superfluids

We deal with the problem of finding an experimentally-doable way of detecting anyons. We focus on cold-atom experiments. The presence of anyons in trapped cold atoms gases can be linked to the measurements of local observables on the ground states of the system. This idea has currently been used to study Fractional Quantum Hall states with quasi-holes excitations. We apply the same reasoning to 2D p-wave superfluids, that can host anyons in vortices in the order parameter. We extend the analytical calculations developed for quasi-holes to vortices, showing that we need the expected values of the angular momentum and particle number observables on the ground state to retrieve the presence of anyons. To validate the conclusions of the analytical calculation we wrote a custom Python code to perform exact diagonalization on the discretized Hamiltonian of the system, in order to retrieve its ground upon which calculate the matrix elements of the observables. In the meanwhile we also discuss various benchmark that we ran on approximate version of the system's Hamiltonian to check for the correct implementation of the algorithm and how the parameters of the simulation were set to obtain to correctly extrapolate the system in the continuum limit. Finally, we discuss several ways we employed to build an angular momentum operator on this system and the issues that arise when trying to compute the ground states expectation values of these lattice operators.