Multi-speed prethermalization in spin models with power-law decaying interactions

Abstract

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 ($1/r^{\alpha }$) interactions for $d$-dimensional lattice spin models with uniaxial symmetry, and show that, in the regime $d<\alpha <d+2$, the entanglement and correlation buildup is radically altered by the existence of a non-linear dispersion relation of quasi-particles, $\omega \sim k^{z<1}$, 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.

6+9 pages, 3+9 figures

References in corpus (9)

• Real time evolution using the density matrix renormalization group
• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• New frontiers with quantum gases of polar molecules
• Nearly-linear light cones in long-range interacting quantum systems
• Quantum correlations and entanglement in far-from-equilibrium spin systems
• Entanglement area laws for long-range interacting systems
• Entanglement and fluctuations in the XXZ model with power-law interactions
• Dynamics of correlations in two-dimensional quantum spin models with long-range interactions: A phase-space Monte-Carlo study
• Investigation of Quantum Phase Transitions using Multi-target DMRG Methods

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