On the Topological Origin of Entanglement in Ising Spin Glasses

Details On the Topological Origin of Entanglement in Ising Spin Glasses On the Topological Origin of Entanglement in Ising Spin Glasses

2006-08-16

arxiv.org/abs/hep-th/0608116v1

Mod.Phys.Lett.A22:201-208,2007

Physics

High Energy Physics

High Energy Physics - Theory

RevTex4, 6 pages

Scientific paper

10.1142/S0217732307022542

The origin of thermal and quantum entanglement in a class of three-dimensional spin models, at low momenta, is traced to purely topological reasons. The establishment of the result is facilitated by the gauge principle which, when used in conjunction with the duality mapping of the spin models, enables us to recast them as lattice Chern-Simons gauge theories. The thermal and quantum entanglement measures are expressed in terms of the expectation values of Wilson lines, loops, and their generalisations. For continuous spins, these are known to yield the topological invariants of knots and links. For Ising-like models, they are expressible in terms of the topological invariants of three-manifolds obtained from finite group cohomology -- the so-called Dijkgraaf-Witten invariants.

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