Application of the generalized 3D JordanWigner transformation to the bilayer Heisenberg antiferromagnet
Abstract
We extend the definition of the JordanWigner transformation to three dimensions using the generalization of ideas that were used in the twodimensional case by one of the present authors. Under this transformation, the 3D XY Hamiltonian is transformed into a system of spinless fermions coupled to a gauge field with only two components. We calculate the flux per plaquette for the 3 elementary perpendicular plaquettes of a cubic lattice, and find that it is nonzero for only two of the plaquettes. We provide a simple interpretation for the average phaseperplaquette being $\pi$ on the plaquettes where it is nonzero. Then we apply these findings to the investigation of the Heisenberg bilayer antiferromagnet.
 Publication:

arXiv eprints
 Pub Date:
 July 2000
 arXiv:
 arXiv:condmat/0007261
 Bibcode:
 2000cond.mat..7261B
 Keywords:

 Condensed Matter  Strongly Correlated Electrons