Topological phases of shaken quantum Ising lattices

Abstract

The quantum compass model consists of a two-dimensional square spin lattice where the orientation of the spin-spin interactions depends on the spatial direction of the bonds. It has remarkable symmetry properties and the ground state shows topological degeneracy. The implementation of the quantum compass model in quantum simulation setups like ultracold atoms and trapped ions is far from trivial, since spin interactions in those sytems typically are independent of the spatial direction. Ising spin interactions, on the contrary, can be induced and controlled in atomic setups with state-of-the art experimental techniques. In this work, we show how the quantum compass model on a rectangular lattice can be simulated by the use of the photon-assisted tunneling induced by periodic drivings on a quantum Ising spin model. We describe a procedure to adiabatically prepare one of the doubly-degenerate ground states of this model by adiabatically ramping down a transverse magnetic field, with surprising differences depending on the parity of the lattice size. Exact diagonalizations confirm the validity of this approach for small lattices. Specific implementations of this scheme are presented with ultracold atoms in optical lattices in the Mott insulator regime, as well as with Rydberg atoms.

10 pages, 3 figures, comments are welcome

References in corpus (10)

• Measuring the Chern number of Hofstadter bands with ultracold bosonic atoms
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• Designing Frustrated Quantum Magnets with Laser-Dressed Rydberg Atoms
• First order phase transition in the anisotropic quantum orbital compass model
• Spin dynamics for bosons in an optical lattice
• Nature of the Quantum Phase Transition in Quantum Compass Model
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Cited by in corpus (3)

• Long-range Heisenberg models in quasi-periodically driven crystals of trapped ions
• Topological edge states in periodically-driven trapped-ion chains
• Stabilization of symmetry-protected long-range entanglement in stochastic quantum circuits