Long-range Heisenberg models in quasi-periodically driven crystals of trapped ions

Abstract

We introduce a theoretical scheme for the analog quantum simulation of long-range XYZ models using current trapped-ion technology. In order to achieve fully-tunable Heisenberg-type interactions, our proposal requires a state-dependent dipole force along a single vibrational axis, together with a combination of standard resonant and detuned carrier drivings. We discuss how this quantum simulator could explore the effect of long-range interactions on the phase diagram by combining an adiabatic protocol with the quasi-periodic drivings and test the validity of our scheme numerically. At the isotropic Heisenberg point, we show that the long-range Hamiltonian can be mapped onto a non-linear sigma model with a topological term that is responsible for its low-energy properties, and we benchmark our predictions with Matrix-Product-State numerical simulations.

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References in corpus (6)

• Towards fault-tolerant quantum computing with trapped ions
• Manipulation and Detection of a Trapped Yb+ Ion Hyperfine Qubit
• Entanglement entropy for the long range Ising chain
• Experimental Realization of a Quantum Integer-Spin Chain with Controllable Interactions
• Optimal Surface-Electrode Trap Lattices for Quantum Simulation with Trapped Ions
• Tunable spin-spin interactions and entanglement of ions in separate wells

Cited by in corpus (8)

• Fidelity Susceptibility Study of Quantum Long-Range Antiferromagnetic Ising Chain
• Boson-mediated quantum spin simulators in transverse fields: XY model and spin-boson entanglement
• Topological edge states in periodically-driven trapped-ion chains
• Boundary driven Heisenberg-chain in the long-range interacting regime: Robustness against far from equilibrium effects
• Magnetic phase diagram and quantum phase transitions in a two-species boson model
• Entanglement entropy of the long-range Dyson hierarchical model
• Self-consistent harmonic approximation with non-local couplings
• Impacts of Intrinsic Noise and Quantum Entanglement on the Geometric and Dynamical Properties of the XXZ Heisenberg Interacting Spin Model