Tommaso Roscilde

The relaxation of uniform quantum systems with finite-range interactions after a quench is generically driven by the ballistic propagation of long-lived quasi-particle excitations triggered by a sufficiently small quench. Here we investigate the case of long-range ($1/r^α$) interactions for $d$-dimensional lattice spin models with uniaxial symmetry, and show that, in the regime $d < α< d+2$, the entanglement and correlation buildup is radically altered by the existence of a non-linear dispersion relation of quasi-particles, $ω\sim k^{z<1}$, at small wave vectors, leading to a divergence of the quasiparticle group velocity and super-ballistic propagation. This translates in a super-linear growth of correlation fronts with time, and sub-linear growth of relaxation times of subsystem observables with size, when focusing on $k=0$ fluctuations. Yet the large dispersion in group velocities leads to an extreme wavelength dependence of relaxation times of finite-$k$ fluctuations, with entanglement being susceptible to the longest of them. Our predictions are directly relevant to current experiments probing the nonequilibrium dynamics of trapped ions, or ultracold magnetic and Rydberg atoms in optical lattices.

We propose loading trapped ions into microtraps formed by an optical lattice. For harmonic microtraps, the Coulomb coupling of the spatial motions of neighboring ions can be used to construct a broad class of effective short-range Hamiltonians acting on an internal degree of freedom of the ions. For large anharmonicities, on the other hand, the spatial motion of the ions itself represents a spin-1/2 model with frustrated dipolar XY interactions. We illustrate the latter setup with three systems: the linear chain, the zig-zag ladder, and the triangular lattice. In the frustrated zig-zag ladder with dipolar interactions we find chiral ordering beyond what was predicted previously for a next-nearest-neighbor model. In the frustrated anisotropic triangular lattice with nearest-neighbor interactions we find that the transition from the one-dimensional gapless spin-liquid phase to the two-dimensional spiraling ordered phase passes through a gapped spin-liquid phase, similar to what has been predicted for the same model with Heisenberg interactions. Further, a second gapped spin-liquid phase marks the transition to the two-dimensional Neel-ordered phase.