Unconstrained tree tensor simulations for high-dimensional quantum many-body simulations

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We present some recent results on the development of efficient unconstrained tree tensor networks algorithms and their application to high-dimensional many-body quantum systems. In particular, we present our results on topological two-dimensional systems, two-dimensional Rydberg atom systems, and two- and three-dimensional lattice gauge theories in presence of fermonic matter. Finally, we present their application to the study of open many-body quantum systems and in particular to the computation of the entanglement of formation in critical many-body quantum systems, resulting in the generalization of the Calabrese-Cardy formula to open systems.