We review some recent results on the development of efficient tree tensor network
algorithms and their applications to high-dimensional many-body quantum systems
and machine learning problems in High Energy Physics.
In particular, we present recent results on two and three-dimensional
lattice gauge theories in presence of fermionic matter at finite densities.
Morevoer, we compute the entanglement of formation in critical many-body
quantum systems at finite temperature, resulting in the generalization of the
logarithmic formula to open systems. Finally, we present an application of tensor
network machine learning to LHCb event classification.