Generalized Jordan-Wigner transformations

We introduce a new spin-fermion mapping, for arbitrary spin S generating th e SU(2) group algebra, that constitutes a natural generalization of the Jor dan-Wigner transformation for S = 1/2. The mapping, valid for regular latti ces in any spatial dimension d, serves to unravel hidden symmetries. We ill ustrate the power of the transformation by finding exact solutions to latti ce models previously unsolved by standard techniques. We also show the exis tence of the Haldane gap in S = 1 bilinear nearest-neighbor Heisenberg spin chains and discuss the relevance of the mapping to models of strongly corr elated electrons. Moreover, we present a general spin-anyon mapping for the case d less than or equal to 2.