The localization of charge carriers by electronic repulsion was suggested by Mott in the 1930s to explain the insulating state observed in supposedly metallic NiO. The Mott metal-insulator transition has been subject of intense investigations ever since-not least for its relation to high-temperature superconductivity. A detailed comparison to real materials, however, is lacking because the pristine Mott state is commonly obscured by antiferromagnetism and a complicated band structure. Here we study organic quantum spin liquids, prototype realizations of the single-band Hubbard model in the absence of magnetic order. Mapping the Hubbard bands by optical spectroscopy provides an absolute measure of the interaction strength and bandwidth-the crucial parameters that enter calculations. In this way, we advance beyond conventional temperature-pressure plots and quantitatively compose a generic phase diagram for all genuine Mott insulators based on the absolute strength of the electronic correlations. We also identify metallic quantum fluctuations as a precursor of the Mott insulator-metal transition, previously predicted but never observed. Our results suggest that all relevant phenomena in the phase diagram scale with the Coulomb repulsion U, which provides a direct link to unconventional superconductivity in cuprates and other strongly correlated materials.

We develop a unified theoretical picture for excitations in Mott systems, portraying both the heavy quasiparticle excitations and the Hubbard bands as features of an emergent Fermi liquid state formed in an extended Hilbert space, which is non-perturbatively connected to the physical system. This observation sheds light on the fact that even the incoherent excitations in strongly correlated matter often display a well defined Bloch character, with pronounced momentum dispersion. Furthermore, it indicates that the Mott point can be viewed as a topological transition, where the number of distinct dispersing bands displays a sudden change at the critical point. Our results, obtained from an appropriate variational principle, display also remarkable quantitative accuracy. This opens an exciting avenue for fast realistic modeling of strongly correlated materials.

We present a unified perspective on Dynamical Mean Field Theory (DMFT), Density-Matrix Embedding Theory (DMET) and Rotationally Invariant Slave Bosons (RISB). We show that DMET can be regarded as a simplification of the RISB method where the quasiparticle weight is set to unity. This relation allows to easily transpose extensions of a given method to another: for instance, a temperature-dependent version of RISB can be used to derive a temperature-dependent free-energy formula for DMET.