Modeling Electron Fractionalization with Unconventional Fock Spaces

It is shown that certain fractionally-charged quasiparticles can be modeled on D−dimensional lattices in terms of unconventional yet simple Fock algebras of creation and annihilation operators. These unconventional Fock algebras are derived from the usual fermionic algebra by taking roots (the square root, cubic root, etc) of the usual fermionic creation and annihilation operators. If the fermions carry non-Abelian charges like spin, then this approach fractionalizes the Abelian charges only. In particular, the mth-root of a spinful fermion is an operator that carries charge e/m and spin 1/2. While the exclusion statics is fixed by the root operation, there are several possible choices of quantum exchange statistics for fermion-root quasiparticles. These choices are tied to the dimensionality D = … 1, 2, 3, of the lattice and the exchange statistics between fermions and fractionalized fermions. As an application of potential mesoscopic interest, I investigate numerically the hybridization of Majorana and parafermion zero-energy edge modes caused by fractionalizing but charge-conserving tunneling.

E. Cobanera, J. Phys.: Condens. Matter 29, 305602 (2017)