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Quantum systems with long-range interactions exhibit superballistic propagation due to nonlinear quasiparticle dispersion. This alters entanglement and correlation buildup, impacting relaxation dynamics in experiments with trapped ions and ultracold atoms.

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Area of Science:

  • Quantum physics
  • Condensed matter physics
  • Statistical mechanics

Background:

  • Uniform quantum systems with finite-range interactions typically relax via ballistic quasiparticle propagation after a quench.
  • Understanding nonequilibrium dynamics in systems with long-range interactions is crucial for experimental advancements.

Purpose of the Study:

  • Investigate the effect of long-range (1/r^α) interactions on quantum system relaxation.
  • Analyze the role of nonlinear quasiparticle dispersion in entanglement and correlation buildup.
  • Predict the behavior of correlation fronts and relaxation times in such systems.

Main Methods:

  • Studied a d-dimensional lattice spin model with uniaxial symmetry and long-range interactions.
  • Analyzed the nonlinear dispersion relation (ω∼k^z<1) of quasiparticles at small wave vectors.
  • Focused on k=0 fluctuations and the impact of group velocity dispersion on relaxation times.

Main Results:

  • Discovered superballistic quasiparticle propagation due to nonlinear dispersion in the regime d<α
  • Observed superlinear growth of correlation fronts and sublinear growth of relaxation times with subsystem size for k=0 fluctuations.
  • Found an extreme wavelength dependence of relaxation times for finite-k fluctuations, affecting entanglement.

Conclusions:

  • Long-range interactions fundamentally alter quantum system relaxation dynamics compared to short-range cases.
  • The nonlinear dispersion relation leads to unique propagation and relaxation behaviors.
  • Predictions are relevant for current experiments with trapped ions and ultracold atoms in optical lattices.