Anyons emerging from fermions with conventional two-body interactions

Emergent anyons are the key elements of the topological quantum computation and topological quantum memory. We study a two-component fermion model with conventional two-body interaction in a fine-tuned external field and show that several subsets in the low-lying excitations obey the same fusion rules as those of the toric code model. Those string-like (or domain wall) excitations whose energy congregates in a small spatial region (a wall) may be thought of as quasiparticles which, in a given subset, obey mutual semionic statistics. We show how to peel off one of such subsets from other degenerate subsets and manipulate anyons in cold dipolar Fermi atoms or cold dipolar fermionic heteronuclear molecules in optical lattices by means of the established techniques.