The Entanglement perspectives on the quantum many body problem

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Background and state of the ArtQuantum many body systems are systems made by several constituent, such as for example materials, made by atoms, or light made by photons or nuclei made by nucleons.Complexity of quantum many body systems Quantum many body systems are described by complex wave functions whose number of parameters increases exponentially with the number of constituents thus effectively limiting our capability to study them.Tensor networks In specific cases, like for example when studying the equilibrium state of many body systems described with local enough Hamiltonians, tensor networks provide a polynomial description of the exponentially large state of many body quantum systems. Tensor networks are constructed from small elementary tensors contracted in a specific pattern dictated by the geometry of the network.Geometry of tensor networks the geometry of the network completely determines the patterns of correlations in the state it describes. For this reason there is a connection between the structure of entanglement at equilibrium and the geometry of the tensor network and tensor networks are best suited to describe local correlations. Out of equilibrium, During the out-of-equilibrium evolution short range correlations radiate into long range correlations and thus traditional tensor networks chase to provide good description of the many body wave function. Research hypothesis and objectives Our objective is to find a possible descriptions of the out-of-equilibrium dynamics of a many body quantum systems in term of tensor networks.We will1) apply the intuition that despite the fact that during the out-of-equilibrium evolution long range entanglement is created, the correlations are still short ranged. In this way we will devise a strategy to perform approximate out of equilibrium of many body quantum states that will allow to get the correct evolutions of local observables.2) characterize and understand advanced tensor network structures such as the spectral tensor networks and the branching MERAs and adapt them to perform the out of equilibrium evolution of quantum systems.