Testing Quantumness: From Artificial Quantum Arrays to Lattice Spin Models and Spin Liquids

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Quantum mechanics is one of the best-confirmed theories in physics. Over the last two decades of steady and spectacular improvements in experimental techniques, there were no indications that quantum mechanics fails even when describing macroscopic systems. We are now at the beginning of a "second quantum revolution'', where significant research efforts are being shifted from understanding quantum mechanical systems to applying essentially quantum properties of macroscopic systems in order to develop new quantum technologies (e.g., in quantum computing). However, direct simulation of large enough systems with quantum mechanical behaviour is practically impossible, because of the astronomical computational resources it requires. Current developments in quantum engineering already brought us to face this barrier. It is therefore necessary to develop a set of approximate approaches, which are nonetheless precise enough, at least on average, to provide the understanding of and a guidance to the development of still larger artificial quantum systems, to the benefit of both fundamental science and cutting edge technology. In addition, magnetic materials, behaving quantum mechanically, require the same treatment with respect to their "quantumness", in this case in the thermodynamic limit. The goal of this project is to develop such a general theory and apply it to a number of important problems.