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Jordan-Wigner transformation for quantum-spin systems in two dimensions and fractional statistics

Jul 17, 1989
Published in:
  • Phys.Rev.Lett. 63 (1989) 3, 322
  • Published: Jul 17, 1989
DOI:
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Abstract: (APS)
I construct a Jordan-Wigner transformation for spin-one-half quantum systems on two-dimensional lattices. I show that the spin-one-half XY (i.e., a hard-core Bose system) is equivalent (on any two-dimensional Bravais lattice) to a system of spinless fermions and gauge fields satisfying the constraint that the gauge flux on a plaquette must be proportional to the spin (particle) density on site. The constraint is enforced by the addition of a Chern-Simons term of strength \ensuremath{\theta} to the Lagrangian of the theory. For the particular value \ensuremath{\theta}=1/2\ensuremath{\pi}, the resulting particles are fermions. In general they are anyons. The implications of these results for quantum spin liquids are briefly discussed.
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