  Proposed is a generalization of Jordan-Wigner transform that allows to
exactly fermionize a large family of quantum spin Hamiltonians in dimensions
higher than one. The key new steps are to enlarge the Hilbert space of the
original model by adding to it a collection of stand-alone free spins and to
use a combination of these auxiliary operators and the lattice spins to
construct a proper fermion representation of the physical Hamiltonian. The
transform is especially useful for lattice spin Hamiltonians, where two-spin
interactions of XY-type are either absent or exist only within one-dimensional
chains and where the chains are coupled via two-spin interactions of Ising
type, ring-exchange terms, or more general multi-spin interactions that involve
an even number of spin operators from each chain. Using the proposed
fermionization method we provide a simple argument suggesting that a spin
Hamiltonian closely-related to the ring-exchange model proposed by Paramekanti,
Balents, and Fisher [Phys. Rev. B 66, 054526 (2002)] indeed realizes a
spin-liquid state.
