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

TL;DR

This paper investigates how the critical dynamics of quantum Ising chains with long-range interactions change from chaotic to sharp as the ramping time of the transverse field increases, highlighting the transition from chaotic to adiabatic behavior.

Contribution

It demonstrates that the chaotic crossover region in long-range quantum Ising chains diminishes with slower ramps, indicating a transition to a sharp phase transition in the adiabatic limit.

Findings

Chaotic crossover region widens with increasing interaction range for abrupt quenches.

The width of the chaotic region decreases with longer ramp times.

In the adiabatic limit, chaos disappears and a sharp transition emerges.

Abstract

Quantum many body systems with long range interactions are known to display many fascinating phenomena experimentally observable in trapped ions, Rydberg atoms and polar molecules. Among these are dynamical phase transitions which occur 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 explore the fate of critical dynamics in Ising chains with long-range interactions when the transverse field is ramped up with a finite speed. While for abrupt quenches we observe a chaotic region that widens as $\alpha$ is increased, the width of the crossover region diminishes as the time of the ramp increases, suggesting that chaos will disappear altogether and be replaced by a sharp transition in the adiabatic limit.