Entanglement production in bosonic systems: Linear and logarithmic growth

TL;DR

This paper analyzes how entanglement entropy evolves over time in bosonic systems, revealing linear, logarithmic, and oscillatory growth patterns depending on the Hamiltonian's stability properties, with numerical evidence extending findings beyond Gaussian states.

Contribution

It classifies quadratic Hamiltonians into stable, unstable, and metastable types, linking each to specific entanglement growth behaviors, and provides numerical evidence for similar entanglement dynamics in non-Gaussian and non-quadratic cases.

Findings

Quadratic Hamiltonians exhibit distinct entanglement growth patterns: linear, logarithmic, or oscillatory.

Numerical results suggest non-Gaussian initial states share asymptotic entanglement behavior with Gaussian states.

Intermediate-time entanglement dynamics are similar even for non-quadratic Hamiltonians.

Abstract

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 production through quadratic Hamiltonians has the same asymptotic behavior for non-Gaussian initial states as for Gaussian ones. Moreover, even for non-quadratic Hamiltonians, we find a similar behavior at intermediate times. Our results are of relevance to understanding entanglement production for quantum fields in dynamical backgrounds and ultracold atoms in optical lattices.