• entanglement
• localization
• quantum complex networks
• quantum information
• quantum many-body
• random hopping
• structural disorder
• tunable-range

Motivated by recent advances in quantum technologies, we investigate entanglement spreading and excitation transport within quantum complex networks.
For this purpose, we adopt a description in which network nodes represent sites of the physical system (e.g. qubits), and links represent pairs of sites coupled by the Hamiltonian [Bentsen et al., Phys Rev Lett (2019)]. We consider a random tunable-range model [Gori et al., Phys Rev E (2017)] which, in terms of only two parameters, encompasses a large variety of graphs and reduces, in limiting cases, to well-studied benchmarks. Then, it is equipped with a paradigmatic Hamiltonian consisting of hopping terms on the network links. Building on known results [Gori et al., Phys Rev E (2017)], we first study the classical case, providing new semi-analytical estimates.
We then address quantum dynamics: For the single-particle case, we analyse the asymptotic entanglement entropy between two halves of the system, computed by Exact Diagonalization. Surprisingly, we observe a new localization region for intermediate ranges of the network links. To understand this phenomenon, we introduce an approximate one-dimensional model and try to relate dynamics to network measures.
The analysis is extended to half-filling using fermionic Gaussian states, obtaining results close to the single-particle ones that raise new interesting questions for future work.
It is concluded that this model exhibits non-trivial behaviour, especially in the region where unexpected localization occurs. We infer that this is determined by the interplay between network features and quantum effects, possibly induced by structural disorder.