ABSTRACT Title of dissertation: DYNAMICS AND EXCITED STATES OF QUANTUM MANY-BODY SPIN CHAINS WITH TRAPPED IONS

Certain classes of quantum many-body systems, including those supporting phenomena like high-Tc superconductivity and spin liquids, are believed to be funda-mentally intractable to classical modeling. Quantum simulations, in which synthetic materials are engineered by inducing well-controlled quantum systems like ultracold atoms to obey many-body Hamiltonians of interest, are a promising new approach to study this type of physics. However, current experiments have not yet simul-taneously achieved the system sizes and the level of control necessary to observe and understand novel physics that cannot be classically modeled. In this work, I present several advances toward this ultimate goal of large-scale, highly controllable quantum simulations of many-body spin physics. We simulate long-range Ising and XY spin models in the presence of transverse and longitudinal magnetic fields using chains of up to 18 ultracold 171Yb+ ions held in a linear Paul trap, where two hy-perfine levels in each ion encode spin-1/2 states. The tunable spin-spin interactions and effective magnetic fields are engineered using laser fields, and the individual spin states are directly imaged with state-dependent fluorescence. The results i