低维晶格上反铁磁海森堡自旋的统一研究
A Uniform Approach to Antiferromagnetic Heisenberg Spins on Low Dimensional Lattices
摘要：
使用群论方法，我们表明，三角形和正方形晶格，在连续极限的反铁磁序参量生活在SO 3不尊重初始晶格。对于反铁磁链，我们恢复了Haldron分解。这个序参量与局部规范场相互作用，而不是像文献中隐含的那样与全局规范场相互作用，在我们的方法中，这种相互作用以一种相当自然的方式出现。事实上，这仅仅对应于自旋群通过局域规范场的一种新的扩展。这种基于实除代数的分析适用于低维格。
英文摘要：
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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