Quantic PhD student Alba Cervera-Lierta and our P.I. José Ignacio Latorre have published a new article on Journal of Physics A: Mathematical and Theoretical.
The article title is “Multipartite entanglement in spin chains and the hyperdeterminant” and the reference is J. Phys. A: Math. Theor. 51 505301 (2018) (arXiv: [quant-ph] 1802.02596).
In this work, they study the multipartite entanglement in spin chains, in particular in the Ising model, XXZ model and Haldane-Shastry model.
As a figure of merit to quantify multipartite entanglement they use the Cayley hyperdeterminant, which is a polynomial constructed with the components of the wave function which is invariant under local unitary transformation. For n=2 and n=3, the hyperdeterminant coincides with the concurrence and the tangle respectively, well known figures of merit for multipartite entanglement. For n=4, Hyperdeterminant is a polynomial of degree 24 that can be written in terms of more simple polynomials, S and T, of degree 8 and 12 respectively.
They observe that these polynomials are able to capture the phase transitions present in the models studied as well as a subclass of quadripartite entanglement present in the eigenstates.
Besides spin chains, they also study the quadripartite entanglement of random states, ground states of random matrix Hamiltonians in the Wigner-Syson Gaussian ensambles and the quadripartite entangled states defined by Vestraete et al in 2002.
This figure shows the hyperdeterminant for the ground state and second excited state of a n=4 Ising spin chain as a function of the transverse magnetic field λ. For an infinite chain, this model has a phase transition at λ=1. As can be seen, the hyperdeterminant peaks close to this phase transition.