"The project “Exploring magnetic quantum phase transitions with ultra-cold Fermi gases” (MAG-QUPT) aims at developing a novel platform for the experimental exploration of quantum phase transitions and quantum critical phenomena using ultra-cold atomic gases. As envisioned by R. Feynman in 1982, and successfully demonstrated in the last years, these systems can be used to emulate fundamental quantum collective phenomena and constitute ideal test-beds for deepening our understanding of quantum-many body physics. By providing novel insights into long-standing open questions of condensed-matter physics, they pave the way towards the development of new materials and quantum devices. The ambitious goal of this research project is to establish a novel toolbox for the controlled study of magnetic quantum phase transitions based on ultra-cold quantum gases, going beyond the capabilities currently offered by solid-state systems. To this end, we will exploit the unique properties of ultra-cold Fermi gases trapped in optical lattices of adjustable geometries. Building-up on our previous work, we will implement paradigmatic spin models for magnetic quantum phase transitions in this setting, and develop novel tools for their characterization. More precisely, this research proposal introduces two main objectives: i) the development of an experimental apparatus specifically adapted to this goal. ii) the experimental observation and characterization of a prototypical magnetic quantum phase transition, and the study of the corresponding quantum critical regime. Reaching these objectives would demonstrate a new frame for the experimental exploration of quantum critical phenomena. This would open new horizons for our understanding of the fundamental connections between quantum many-body physics and entanglement, with potential applications in the development of novel quantum technologies."