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 test bed 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 we provide a detailed discussion of its experimental feasibility.