  We investigate theoretically systems of ions in segmented linear Paul traps
for the quantum simulation of quantum spin models with tunable interactions.
The scheme is entirely general and can be applied to the realization of
arbitrary spin-spin interactions. As a specific application we discuss in
detail the quantum simulation of models that exhibit long-distance entanglement
in the ground state. We show how tailoring of the axial trapping potential
allows for generating spin-spin coupling patterns that are suitable to create
long-distance entanglement. We discuss how suitable sequences of microwave
pulses can implement Trotter expansions and realize various kinds of effective
spin-spin interactions. The corresponding Hamiltonians can be varied on
adjustable time scales, thereby allowing the controlled adiabatic preparation
of their ground states.
