Speaker
Description
Trapped ions in a periodic potential are a paradigm of a frustrated Wigner crystal. The dynamics are captured by a long-range Frenkel-Kontorova model. We show that the classical ground state can be mapped to the one of a long-range Ising spin chain in a magnetic field, whose strength is determined by the mismatch between the chain’s and substrate lattice’s periodicity. The mapping is exact when the substrate potential is a piecewise harmonic potential and holds for any two-body interaction decaying as $1/r^\alpha$ with the distance $r$. We show that the ground state is a devil’s staircase of regular, periodic structures as a function of the mismatch and of the interaction exponent $\alpha$. The predictions of the piecewise parabolic potentials are compared with the case when the substrate is a sinusoidal potential.
| Academic level | PhD student |
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