Quantum entanglement: The unitary 8-vertex braid matrix with imaginary rapidity

TL;DR

This paper investigates how unitary 8-vertex braid matrices with imaginary rapidity induce quantum entanglement on product states, revealing complex relationships between topological and quantum entanglement through elliptic functions.

Contribution

It demonstrates the unitarity of 8-vertex braid matrices with imaginary spectral parameters and explores their entanglement properties using elliptic functions.

Findings

Unitary 8-vertex braid matrices induce quantum entanglement.

Elliptic functions' properties lead to a rich entanglement structure.

The study links topological features with quantum entanglement.

Abstract

We study quantum entanglements induced on product states by the action of 8-vertex braid matrices, rendered unitary with purely imaginary spectral parameters (rapidity). The unitarity is displayed via the "canonical factorization" of the coefficients of the projectors spanning the basis. This adds one more new facet to the famous and fascinating features of the 8-vertex model. The double periodicity and the analytic properties of the elliptic functions involved lead to a rich structure of the 3-tangle quantifying the entanglement. We thus explore the complex relationship between topological and quantum entanglement.