Quantum simulation and many-body physics with hundreds of trapped ions

By employing forces that depend on the internal electronic state (or spin) of an atomic ion, the Coulomb potential energy of a trapped ion crystal can be modified in a spin-dependent way to mimic effective quantum spin Hamiltonians. We use simple models to explain how effective Ising interactions are engineered with trapped-ion crystals. We discuss the range of interactions that can be readily generated and an experimental implementation using single-plane ion crystals in a Penning trap.