Trapped-ion quantum simulation of tunable-range Heisenberg chains

Abstract

Quantum-optical techniques allow for generating controllable spin-spin interactions between ions, making trapped ions an ideal quantum simulator of Heisenberg chains. A single parameter, the detuning of the Raman coupling, allows to switch between ferromagnetic and antiferromagnetic chains, and to modify the range of the interactions. On the antiferromagnetic side, the system can be tuned from an extreme long-range limit, in which any pair of ions interacts with almost equal strength, to interactions with a $1/r^3$ decay. By exact diagonalization, we study how a system of up to 20 ions behaves upon tuning the interactions. We find that it undergoes a transition from a dimerized state with extremely short-ranged correlations towards a state with quasi long-range order, that is, algebraically decaying correlations. On the ferromagnetic side of the system, we demonstrate the feasibility of witnessing non-locality of quantum correlations.

9 pages, 5 figures

References in corpus (3)

• The Magnus expansion and some of its applications
• Entanglement entropy for the long range Ising chain
• Entanglement in the Majumdar-Ghosh model

Cited by in corpus (3)

• The deformed Inozemtsev spin chain
• Strong Disorder Renormalization Group Method for Bond Disordered Antiferromagnetic Quantum Spin Chains with Long Range Interactions: Ground State Properties
• Strong Disorder Renormalization Group Method for Bond Disordered Antiferromagnetic Quantum Spin Chains with Long Range Interactions: Excited States and Finite Temperature Properties