Dynamical Evolution of Entanglement in Disordered Oscillator Systems

• URL: http://arxiv.org/abs/2104.13825v3
• Date: Wed, 12 Oct 2022 05:09:38 GMT
• Title: Dynamical Evolution of Entanglement in Disordered Oscillator Systems
• Authors: Houssam Abdul-Rahman
• Abstract summary: 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.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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