Generalization of the Jordan-Wigner transformation in three dimensions andits application to the Heisenberg bilayer antiferromagnet - art. no. 054410

We extend the definition of the Jordan-Wigner transformation to three dimen sions using the generalization of ideas that were introduced in the two-dim ensional case by one of the present authors. Under this transformation, the three-dimensional XY spin Hamiltonian is mapped onto a system of spin-less fermions coupled to a gauge field with only two nonzero components. This g auge field is calculated explicitly. Then we apply this transformation to t he investigation of the Heisenberg bilayer antiferromagnet. The interesting quantum disordered state realized in this material for strong interlayer c ouplings is studied in detail. We define the physical parameter that govern s this state, and calculate analytically several quantities, such as the gr ound-state energy and the energy gap as a function of the interlayer coupli ng. Very good agreement with existing results and with the infinite interla yer coupling limit is recovered.