## Curvature of spin networks    [PDF]

Edmond Jonckheere, Frank Langbein, Sophie Schirmer
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.
View original: http://arxiv.org/abs/1202.2556