Fractal ground state of ion chains in periodic potentials
arxiv(2024)
摘要
Trapped ions in a periodic potential are a paradigm of a frustrated Wigner
crystal. The dynamics is captured by a long-range Frenkel-Kontorova model. The
classical ground state can be mapped to the one of an antiferromagnetic spin
chain with long-range interactions in a magnetic field, whose strength is
determined by the mismatch between 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^α with
the distance r. The ground state is a devil's staircase of regular, periodic
structures as a function of the mismatch, whose range of stability depends also
on the coefficient α. While the staircase is well defined in the
thermodynamic limit for α>1, for Coulomb interactions, α=1, it
disappears and the sliding-to-pinned transitions becomes crossovers. However,
due to the logarithmic convergence to the thermodynamic limit characteristic of
the Coulomb potential, the staircase is found for any finite number of ions. We
discuss the experimental parameters as well as the features that allow one to
observe and reveal our predictions in experimental platforms. These dynamics
are a showcase of the versatility of trapped ion platforms for exploring the
interplay between frustration and interactions.
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