On the Topological Origin of Entanglement in Ising Spin Glasses

TL;DR

This paper reveals that thermal and quantum entanglement in 3D spin models, including Ising spin glasses, originates from topological properties, linking entanglement measures to topological invariants via gauge theory and duality mappings.

Contribution

It demonstrates the topological origin of entanglement in spin glasses by connecting it to lattice Chern-Simons theories and topological invariants, providing a new theoretical framework.

Findings

Entanglement measures relate to Wilson line and loop expectation values.

Topological invariants of knots, links, and three-manifolds characterize entanglement.

The approach applies to both continuous and Ising-like spins.

Abstract

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.