Diffusive entanglement growth in a monitored harmonic chain

TL;DR

This paper investigates how entanglement grows diffusively in a monitored harmonic chain with smeared measurements, revealing a $t^{1/2}$ growth law and an area-law relaxation, explained by a modified quasiparticle picture involving non-Hermitian modes.

Contribution

It introduces a modified quasiparticle model with non-Hermitian modes to explain diffusive entanglement growth in monitored harmonic chains with large measurement scales.

Findings

Entanglement grows as $t^{1/2}$ for large measurement scales.

Entropy relaxes to an area-law value at late times.

Quasiparticles have finite velocity and a $1/k^2$ lifetime, explaining the growth law.

Abstract

We study entanglement growth in a harmonic oscillator chain subjected to the weak measurement of observables which have been smeared-out over a length scale $R$. We find that entanglement grows diffusively ($S \sim t^{1/2}$) for a large class of initial Gaussian states provided the measurement scale $R$ is sufficiently large. At late times $t \gtrsim \mathcal{O}(L^{2})$ the entropy relaxes towards an area-law value which we compute exactly. We propose a modified quasi-particle picture which accounts for all of these main features and agrees quantitatively well with our essentially exact numerical results. The quasiparticles are associated with the modes of a non-Hermitian effective Hamiltonian. At small wave-vector $k$, the quasiparticles transport entropy with a finite velocity, but have a lifetime scaling as $1/k^2$; the concurrence of these two conditions leads directly to the observed $t^{1/2}$ growth.