Logarithmic growth of entanglement entropy in long-range systems
This event is part of the Biophysics/Condensed Matter Seminar Series.
A number of recent studies of out-of-equilibrium quantum spin systems with long-range interactions have reported numerical evidence of logarithmic growth in time of bipartite entanglement entropy [1,2]. However, an analytical understanding of this observation is apparently lacking. In this talk, I will derive the analytical relation between bipartite entanglement entropy and collective spin-squeezing in long-range spin systems in and out of equilibrium, and use it to elucidate the mechanism responsible for the logarithmic growth in time of entanglement entropy after a quench, which has been numerically observed in a number of recent studies. I will further discuss the special cases of quenches to dynamical critical points, in which entanglement entropy increases linearly in time rather than logarithmically, and relate these behaviors to the structure of the underlying semiclassical trajectories. All our analytical results agree with exact numerical computations, and extend to systems with algebraically-decaying interactions with exponent α ≤ d, where d is the system dimensionality. Our findings also provide access to experimental measurements of entanglement entropy in this class of systems.
 J Schachenmayer, BP Lanyon, CF Roos, AJ Daley - Physical Review X, 2013  A. S. Buyskikh, M. Fagotti, J. Schachenmayer, F. Essler, and A. J. Daley, Phys. Rev. A 93, 053620 (2016).  A.Lerose and S. Pappalardi. "Logarithmic growth of entanglement entropy in out-of-equilibrium long-range systems." arXiv preprint arXiv:1811.05505(2018).