Curvature of spin networks

Details Curvature of spin networks Curvature of spin networks

2012-02-12

arxiv.org/abs/1202.2556v1

Physics

Mathematical Physics

ca 6 pages, accepted for ISCCSP 2012

Scientific paper

We develop a geometric approach to spin networks with Heisenberg or XX coupling. Geometry is acquired by defining a distance on the discrete set of spins. The key feature of the geometry of such networks is their Gauss curvature $\kappa$, viewed here as the ability to isometrically embed the chain in the standard Riemannian manifold of curvature $\kappa$. Here we focus on spin rings. Even though their visual geometry is trivial, it turns out that the geometry they acquire from the quantum mechanical distance is far from trivial.

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