  Entanglement properties of the trial many-body wave functions in variational
treatments of the transverse Ising model in two, three, and four dimensions are
investigated. Based on data for magnetizations and correlation functions
generated by for symmetry-breaking Hartree-Jastrow trial ground states, results
are presented for several measures of bipartite entanglement, including the von
Neumann entropy of a single spin in the lattice, the concurrence between two
spins, and a lower bound on the localizable entanglement, as functions of
coupling strength. A simple relation is established between the Hartree-Jastrow
states and the nilpotent polynomial representation of multipartite
entanglement. In addition, some general comments are made on the entanglement
properties of classes of many-body wave functions commonly adopted in theories
of strongly correlated quantum systems.
