Spin-Peierls Quantum Phase Transitions in Coulomb Crystals

The spin-Peierls instability describes a structural transition of a crystal due to strong magnetic interactions. Here we demonstrate that cold Coulomb crystals of trapped ions provide an experimental testbed in which to study this complex many-body problem and to access extreme regimes where the instability is triggered by quantum fluctuations alone. We present a consistent analysis based on different analytical and numerical methods, and provide a detailed discussion of its feasibility on the basis of ion-trap experiments. Moreover, we identify regimes where this quantum simulation may exceed the power of classical computers.