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Quantum many body systems with long range interactions are known to displaymany fascinating phenomena experimentally observable in trapped ions, Rydbergatoms and polar molecules. Among these are dynamical phase transitions whichoccur after an abrupt quench in spin chains with interactions decaying as$r^{-\alpha}$ and whose critical dynamics depend crucially on the power$\alpha$: for systems with $\alpha<1$ the transition is sharp while for$\alpha>1$ it fans out in a chaotic crossover region. In this paper we explorethe fate of critical dynamics in Ising chains with long-range interactions whenthe transverse field is ramped up with a finite speed. While for abruptquenches we observe a chaotic region that widens as $\alpha$ is increased, thewidth of the crossover region diminishes as the time of the ramp increases,suggesting that chaos will disappear altogether and be replaced by a sharptransition in the adiabatic limit.

Crossover from fast to slow dynamics in quantum Ising chains with long range interactions