  We employ a nuclear magnetic resonance (NMR) quantum information processor to
simulate the ground state of an XXZ spin chain and measure its NMR analog of
entanglement, or pseudo-entanglement. The observed pseudo-entanglement for a
small-size system already displays singularity, a signature which is
qualitatively similar to that in the thermodynamical limit across quantum phase
transitions, including an infinite-order critical point. The experimental
results illustrate a successful approach to investigate quantum correlations in
many-body systems using quantum simulators.
