Exact representation of the large- U Hubbard model and its application

An exact representation of the large-[ital U] Hubbard model is developed in terms of fermionic holon, fermionic doublon, and local spin operators which requires no constraint between the charge and spin operators. The Hamiltonian in the new representation explicitly expresses the Nagaoka theorem, and there is an exact one to one correspondence between the new representation and the large-[ital U] Lieb-Wu wave function for the case of one dimension. Using the new representation, we further show that the signature of spin-charge separation, in any dimension, is the characteristic wave vector 2[bold k][sub [ital F]][sup SF] in the static density-density correlation function ([bold k][sub [ital F]][sup SF] encloses a Fermi volume filled by 1[minus][ital x] spinless fermions per site, where [ital x] is the doping concentration). In addition, we derive the corresponding representation for the [ital t]-[ital J]-[ital J][prime] model, where the [ital J][prime] term describes the indirect hopping of the electrons, and the holon (doublon) propagator which explicitly shows the dependence of charge propagation on the spin state.