Mapping spin - charge separation without constraints

The general form of a mapping of the spin and charge degrees of freedom of electrons onto spinless fermions and local 'spin'-1 2 operators is derived. The electron Hilbert space is mapped onto a tensor product spin-charge Hilbert space. The single occupancy condition of the t-J model is satisfied exactly without the constraints between the operators required with slave particle methods and the size of the Hilbert space (four states per site) is conserved. The connection and distinction between the physical electron spin and the " pseudospin " used in these maps is made explicit. Specifically the pseudospin generates rotations both in spin space and particle-hole space. A geometric description (up to sign) is provided using two component spinors. The form of the mapped t-J Hamiltonian involves the coupling of spin and spinless fermion currents, as one expects. The 2D Hubbard model and the t-J model are two of the most intensely studied models in condensed matter physics. It has been argued that these models provide the minimal description of the CuO 2 planes common to all the cuprate superconductors [1]. In one dimension the Hubbard model can be solved exactly and the ground state is not a Fermi liquid but shows separation of spin and charge degrees of freedom [2]. It has been suggested [3] that this spin-charge separation may also occur in two dimensions and is responsible for the unusual normal state properties found in the cuprate superconductors. The size of the magnetic moments in the undoped cuprates implies that the Hubbard model should be regarded as in the strong coupling limit. In that case, to order t 2 /U , we may use the t-J model. We write the t-J model as follows