Entanglement production in bosonic systems: Linear and logarithmic growth
Lucas Hackl, Eugenio Bianchi, Ranjan Modak, Marcos Rigol
PHYSICAL REVIEW A | AMER PHYSICAL SOC | Published : 2018
We study the time evolution of the entanglement entropy in bosonic systems with time-independent, or time-periodic, Hamiltonians. In the first part, we focus on quadratic Hamiltonians and Gaussian initial states. We show that all quadratic Hamiltonians can be decomposed into three parts: (a) unstable, (b) stable, and (c) metastable. If present, each part contributes in a characteristic way to the time dependence of the entanglement entropy: (a) linear production, (b) bounded oscillations, and (c) logarithmic production. In the second part, we use numerical calculations to go beyond Gaussian states and quadratic Hamiltonians. We provide numerical evidence for the conjecture that entanglement ..View full abstract
Awarded by NSF
Awarded by Army Research Office
L.H. thanks G. De Palma, A. Werner, and J. Eisert for discussions. This work was supported by NSF Grants No. PHY-1404204 (E.B.) and No. PHY-1707482 (M.R.), a Frymoyer fellowship, and a Mebus fellowship (L.H.), by the Army Research Office Grant No. W911NF1410540 (R.M. and M.R.). The computations were carried out at the Institute for CyberScience at Penn State. This research was supported in part by the Perimeter Institute for Theoretical Physics.