Some thermodynamical properties of solids, such as heat capacity and magnetic susceptibility, have recently been shown to be linked to the amount of entanglement in a solid. However, this entanglement may appear a mere mathematical artefact of the typical symmetrization procedure of many-body wavefunction in solid state physics. Here we show that this entanglement is physical, demonstrating the principles of its extraction from a typical solid-state system by scattering two particles off the system. Moreover, we show how to simulate this process using present day optical lattice technology. This demonstrates not only that entanglement exists in solids but also that it can be used for quantum information processing or as a test of Bell's inequalities.
Multipartite entanglement, measured by the geometric entanglement(GE), is discussed for integer spin Valance-Bond-Solid (VBS) state respectively with periodic boundary condition(PBC) and open boundary condition(OBC) in this paper. The optimization in the definition of geometric entanglement can be reduced greatly by exploring the symmetry of VBS state, and then the fully separable state can be determined explicitly. Numerical evaluation for GE by the random simulation is also implemented in order to demonstrate the validity of the reductions. Our calculations show that GE is saturated by a finite value with the increment of particle number, that means that the total entanglement for VBS state would be divergent under the thermodynamic limit. Moreover it is found that the scaling behavior of GE with spin number
s is fitted as
αlog(s+sβ+γ)+δ, in which the values of the parameters
α,β,γ,σ are only dependent on the parity of spin
s. A comparison with entanglement entropy of VBS state is also made, in order to demonstrate the essential differences between multipartite and bipartite entanglement in this model.