Dual trapped-ion quantum simulators: an alternative route towards exotic quantum magnets

Abstract

We present a route towards the quantum simulation of exotic quantum magnetism in ion traps by exploiting dual relations between different spin models. Our strategy allows one to start from Hamiltonians that can be realized with current technology, while properties of an exotic dual model are inferred from measurements of non-local, string-order-like, operators. The latter can be achieved from fluorescence, or from certain spectroscopic measurements, both of which can be combined with finite-size scaling by controlling the number of ions in the dual quantum simulator. We apply this concept to propose quantum simulators of frustrated quantum magnets, and Ising models with multi-spin interactions. We test the validity of the idea by showing numerically that the predictions of an ideal dual quantum simulator are not qualitatively modified by relevant perturbations that occur naturally in the trapped-ion scenario.

14 pages, 7 figures

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• Emerging 2D Gauge theories in Rydberg configurable arrays
• Long-range Heisenberg models in quasi-periodically driven crystals of trapped ions
• Boson-mediated quantum spin simulators in transverse fields: XY model and spin-boson entanglement
• Quantum simulator of link models using spinor dipolar ultracold atoms
• Chiral spin currents in a trapped-ion quantum simulator using Floquet engineering
• Quantum Transport of Energy in Controlled Synthetic Quantum Magnets
• Semiclassical approach to finite temperature quantum annealing with trapped ions