Global quench dynamics and the growth of entanglement entropy in disordered spin chains with tunable range interactions

The nonequilibrium dynamics of disordered many-body quantum systems after a quantum quench unveils important insights about the competition between interactions and disorder, yielding, in particular, an interesting perspective toward the understanding of many-body localization. Still, the experimentally relevant effect of bond randomness in long-range interacting spin chains on their dynamical properties have so far not been investigated. In this Letter, we examine the entanglement entropy growth after a global quench in a quantum spin chain with randomly placed spins and long-range tunable interactions decaying with distance with power alpha. Using a dynamical version of the strong disorder renormalization group we find for alpha > alpha(c) that the entanglement entropy grows logarithmically with time and becomes smaller with larger alpha as S(t) = S-p ln(t)/(2 alpha). Here, S-p = 2 ln 2 - 1. We present results of numerical exact diagonalization calculations for system sizes up to N similar to 16 spins, in good agreement with the analytical results for sufficiently large alpha > alpha(c) approximate to 1.8. For alpha < alpha(c), we find that the entanglement entropy grows as a power law with time, S(t) similar to t(gamma(alpha)) with 0 < gamma(alpha) < 1 a decaying function of the interaction exponent alpha.