A Uniform Approach to Antiferromagnetic Heisenberg Spins on Low Dimensional Lattices

Details A Uniform Approach to Antiferromagnetic Heisenberg Spins on Low Dimensional Lattices A Uniform Approach to Antiferromagnetic Heisenberg Spins on Low Dimensional Lattices

2000-04-24

arxiv.org/abs/math-ph/0004029v2

Phys. Lett. A 276 (2000) p175

Physics

Mathematical Physics

5 pages; REVTeX3

Scientific paper

10.1016/S0375-9601(00)00641-1

Using group theoretical methods we show for both the triangular and square lattices that in the continuum limit the antiferromagnetic order parameter lives on SO3 without respect of the initial lattice. For the antiferromagnetic chain we recover the Haldane decomposition. This order parameter interacts with a local gauge field rather than with a global one as implicitly suggested in the literature which in our approach appears in a rather natural manner. In fact this merely corresponds to a novel extension of the spin group by a local gauge field. This analysis based on the real division algebras applies to low dimensional lattices.

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