Characterizing Genuine Multisite Entanglement in Isotropic Spin Lattices

We consider a class of large superposed states, obtained from dimer coverings on spin-$1/2$ isotropic lattices, whose potential usefulness ranges from organic molecules to quantum computation. We show that they are genuinely multiparty entangled, irrespective of the geometry and dimension of the isotropic lattice. We then present an efficient method to characterize the genuine multisite entanglement in the case of isotropic square spin-$1/2$ lattices, with short-range dimer coverings. We use this iterative analytical method to calculate the multisite entanglement of finite-sized lattices, which through finite-size scaling, enables us to obtain the estimate of the multisite entanglement of the infinite square lattice. The method can be a useful tool to investigate other single- and multisite properties of such states.

Figure 1

The behavior of GGM in the case of a square spin-$1/2$ lattice, with increasing total number of spins ($2N$).