Long-range Heisenberg models in quasiperiodically driven crystals of trapped ions

A. Bermudez, L. Tagliacozzo, G. Sierra, P. Richerme

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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 longrange
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.
Original languageEnglish
Number of pages14
JournalPhysical Review B (Condensed Matter)
Volume95
Issue number2
DOIs
Publication statusPublished - 30 Jan 2017

Keywords

  • analog quantum simulation
  • trapped-ion
  • Heisenberg-type interactions
  • state-dependent dipole force
  • standard resonant
  • detuned carrier drivings
  • longrange interactions
  • adiabatic protocol
  • quasi-periodic drivings

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