New mapping for particles on lattices with hard-core interactions

A novel mapping between Hilbert spaces of unequal dimensionalities yields many-body states which exactly satisfy the no-double-occupancy constraints for particles on lattices in arbitrary spatial dimensions. After proving the states are complete, we apply them to Nagaoka's theorem and the t-J model. Modifications are suggested suitable for spin- 1/2 Heisenberg or X-Y models and for hard-core bosons. Extensions to "soft-core" potentials such as the Hubbard model, or spin problems for spins >1/2 , are also indicated.