Intermediate statistics in two space dimensions in a lattice-regularized Hamiltonian quantum field theory

The non-compact Abelian Higgs model with a Chern-Simons term added is investigated within a Hamiltonian formalism, regularized by a spatial lattice. Transmutted matter fields are constructed, which show intermediate statistics interpolating continuously between the Bose and the Fermi case. Their unbounded localization properties are analyzed in detail. Moreover, the braid structure emerging, when exchanges in a product of transmuted fields are performed, is disclosed.