Dynamical Evolution of Entanglement in Disordered Oscillator Systems

TL;DR

This paper investigates how entanglement evolves in disordered harmonic oscillator systems on a lattice, showing that under localization conditions, entanglement remains bounded by an area law over time, with growth depending on lattice structure.

Contribution

It demonstrates that in localized disordered oscillator systems, entanglement dynamics follow an area law and depend on the lattice tiling structure, providing new insights into non-equilibrium quantum behavior.

Findings

Entanglement follows an area law in localized regimes.

Entanglement growth depends on the lattice tiling and dual graph degree.

Bounded entanglement persists over time in the studied systems.

Abstract

We study the non-equilibrium dynamics of a disordered quantum system consisting of harmonic oscillators in a $d$-dimensional lattice. If the system is sufficiently localized, we show that, starting from a broad class of initial product states that are associated with a tiling (decomposition) of the $d$-dimensional lattice, the dynamical evolution of entanglement follows an area law in all times. Moreover, the entanglement bound reveals a dependency on how the subsystems are located within the lattice in dimensions $d\geq 2$. In particular, the entanglement grows with the maximum degree of the dual graph associated with the lattice tiling.