2000/07/15 by Bounghun Bock, B. Bock, Bock, B. +3
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Magnetic properties of thin films #Nonlinear Dynamics and Pattern Formation #Strongly Correlated Electrons (cond-mat.str-el) #Theoretical and Computational Physics #cond-mat.str-el
paper · pdf · doi:10.48550/arxiv.cond-mat/0007261
arxiv created 2000/07/15 · openalex publication_date 2000/07/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend the definition of the Jordan-Wigner transformation to three dimensions using the generalization of ideas that were used in the two-dimensional 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 phase-per-plaquette being π on the plaquettes where it is nonzero. Then we apply these findings to the investigation of the Heisenberg bilayer antiferromagnet.