Entanglement production in bosonic systems: Linear and logarithmic growth

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.

15+6 pages, 7 figures

References in corpus (19)

• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• Many body localization in Heisenberg XXZ magnet in a random field
• Entanglement in continuous variable systems: Recent advances and current perspectives
• Reheating in Inflationary Cosmology: Theory and Applications
• Nonperturbative Dynamics Of Reheating After Inflation: A Review
• Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
• Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
• Holographic Evolution of Entanglement Entropy
• An acoustic analog to the dynamical Casimir effect in a Bose-Einstein condensate
• Quantum quenches in the many-body localized phase
• "Cosmological" quasiparticle production in harmonically trapped superfluid gases
• Entanglement in a periodic quench
• Chaotic behavior in classical Yang-Mills dynamics
• Quantum quenches and many-body localization in the thermodynamic limit
• Entanglement entropy production in gravitational collapse: covariant regularization and solvable models
• Entropy of a subalgebra of observables and the geometric entanglement entropy
• Entanglement dynamics following a sudden quench: an exact solution
• The multi-mode quantum Entropy Power Inequality

Cited by in corpus (38)

• Complexity and entanglement for thermofield double states
• Entanglement spreading in a minimal model of maximal many-body quantum chaos
• Bridging entanglement dynamics and chaos in semiclassical systems
• Geometry of variational methods: dynamics of closed quantum systems
• Entanglement spreading in non-equilibrium integrable systems
• Origin of the slow growth of entanglement entropy in long-range interacting spin systems
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Entanglement revivals as a probe of scrambling in finite quantum systems
• Spreading of entanglement and correlations after a quench with intertwined quasiparticles
• Towards a Generalized Hydrodynamics description of Rényi entropies in integrable systems
• Rényi entropies of generic thermodynamic macrostates in integrable systems
• Entanglement in a dephasing model and many-body localization
• Relaxation to gaussian and generalized Gibbs states in systems of particles with quadratic hamiltonians
• Dynamical manifestation of Gibbs paradox after a quantum quench
• Many-body dynamical phase transition in quasi-periodic potential
• Quenching from superfluid to free bosons in two dimensions: entanglement, symmetries, and quantum Mpemba effect
• Entanglement production in the dynamical Casimir effect at parametric resonance
• Prethermalisation and Thermalisation in the Entanglement Dynamics
• Minimal energy cost of entanglement extraction
• Subsystem complexity after a global quantum quench
• Surprises in the Deep Hilbert Space of all-to-all systems: From super-exponential scrambling to slow entanglement growth
• Real-space quantum-to-classical transition of time dependent background fluctuations
• Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states
• Dynamical scaling symmetry and asymptotic quantum correlations for time-dependent scalar fields
• The Interplay of Finite and Infinite Size Stability in Quadratic Bosonic Lindbladians
• Bosonic and fermionic Gaussian states from Kähler structures
• Quasi-particle spectrum and entanglement generation after a quench in the quantum Potts spin chain
• Quantum walk on a graph of spins: magnetism and entanglement
• Statistical and dynamical aspects of quantum chaos in a kicked Bose-Hubbard dimer
• Measurement-induced phase transition in free bosons
• Probing chaos in the spherical p-spin glass model
• Entanglement Dynamics between Ising Spins and a Central Ancilla
• Entanglement entropy on finitely ramified graphs
• Uncovering measurement-induced entanglement via directional adaptive dynamics and incomplete information
• The generalized strong subadditivity of the von Neumann entropy for bosonic quantum systems
• Thermalization in parametrically driven coupled oscillators
• Odd Entanglement Entropy and Logarithmic Negativity for Thermofield Double States
• Entanglement entropy dynamics of non-Gaussian states in free boson systems: Random sampling approach