Quantum Simulation of the Haldane Phase Using Trapped Ions

Abstract

A proposal to use trapped ions to simulate spin-one XXZ antiferromagnetic (AFM) chains as an experimental tool to explore the Haldane phase is presented. We explain how to reach the Haldane phase adiabatically, demonstrate the robustness of the ground states to noise in the magnetic field and Rabi frequencies, and propose a way to detect them using their characterizations: an excitation gap and exponentially decaying correlations, a nonvanishing nonlocal string order and a double degenerate entanglement spectrum. Scaling up to higher dimensions and more frustrated lattices, we obtain richer phase diagrams, and we can reach spin liquid phase, which can be detected by its entanglement entropy which obeys the boundary law.

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• Fully robust qubit in atomic and molecular three-level systems
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• Quantum Algorithms for Quantum Chemistry based on the sparsity of the CI-matrix
• Universal Set of Gates for Microwave Dressed-State Quantum Computing
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• Interaction induced fractionalization and topological superconductivity in the polar molecules anisotropic $t-J$ model
• Constructing the spin-1 Haldane phase on a qudit quantum processor
• Hidden Magnetism in Periodically Modulated One Dimensional Dipolar Fermions
• Spin-1 Haldane phase in a chain of Rydberg atoms
• String order via Floquet interactions in atomic systems
• Achieving continuously tunable critical exponents for long-range spin systems simulated with trapped ions
• Robust symmetry-protected metrology with the Haldane phase
• Proposal for high-fidelity quantum simulation using a hybrid dressed state
• Quantum phase transitions in spin-1 compass chains
• Quantum Simulation of Spin-1 XXZ-Heisenberg Models and the Haldane Phase with Dysprosium
• Quantum simulation of superexchange magnetism in linear ion crystals
• Robust entanglement by continuous dynamical decoupling of the J-coupling interaction