Curvature of quantum rings

Abstract

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.

Communications, Control and Signal Processing (ISCCSP), 2012, 5th International Conference of (Rome, 2012)

References in corpus (1)

• Geometry and Curvature of Spin Networks

Cited by in corpus (5)

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• Structured singular value analysis for spintronics network information transfer control
• Quantum networks: Anti-core of spin chains
• Characterization and Control of Quantum Spin Chains and Rings