Strong quantum correlations lie in the center of many fascinating physical phenomena, as for instance quantum phase transitions. A direct way to study quantum correlations in many body systems is to compute certain observables with the respective wave function. Yet, it is known that reduced density matrices are able to describe and predict directly the bulk of physical features of such quantum phenomena, overcoming the curse of dimensionality of wave-function-based theories. Based on a generalization of Hohenberg-Kohn’s theorem for electronic systems, we have recently proposed a new kind of functional theories of quantum correlations for many-body systems [1]. Since these functional theories involve the one-body reduced density matrix as a variable but still recovers quantum correlations in an exact way they are particularly well suited for the accurate description of condensates, superconductors, or bosonic mixtures in the relevant regimes of supersolidity and droplets. In this talk I will introduce the scope of those functional theories and give concrete examples for the case of Hubbard Hamiltonians. I will also show how recent developments in machine learning are helping to understand and approximate those universal functionals.
[1] CL Benavides-Riveros et alt., PRL 124, 180603 (2020); PRL 129, 066401 (2022).