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

Amitabha Chakrabarti (1) , Anirban Chakraborti (2) , Aymen Jedidi (2)

1 CPHT - Centre de Physique Théorique [Palaiseau]
2 MAS - Mathématiques Appliquées aux Systèmes - EA 4037

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.

Domaines: Mécanique statistique [cond-mat.stat-mech]; Physique Quantique [quant-ph]

Amitabha Chakrabarti, Anirban Chakraborti, Aymen Jedidi. Quantum entanglement: The unitary 8-vertex braid matrix with imaginary rapidity. Journal of Physics A: Mathematical and Theoretical, 2010, 43, pp.482001. ⟨10.1088/1751-8113/43/48/482001⟩. ⟨hal-00827939⟩