Entanglement Dynamics in Harmonic Oscillator Chains

TL;DR

This paper investigates how bipartite entanglement evolves over time in gapped harmonic oscillator chains, revealing linear growth in entanglement entropy that challenges efficient simulation methods.

Contribution

It derives a lower bound for entanglement growth and demonstrates that entanglement increases at least linearly, impacting simulation strategies for such systems.

Findings

Entanglement entropy grows at least linearly over time.

A lower bound for von Neumann entropy is established.

Simulation of gapped harmonic systems is computationally challenging.

Abstract

We study the long-time evolution of the bipartite entanglement in translationally invariant gapped harmonic lattice systems with finite-range interactions. A lower bound for the von Neumann entropy is derived in terms of the purity of the reduced density matrix. It is shown that starting from an initially Gaussian state the entanglement entropy increases at least linearly in time. This implies that the dynamics of gapped (non-critical) harmonic lattice systems cannot be efficiently simulated by algorithms based on matrix-product decompositions of the quantum state.