Unraveling the Mott-Peierls intrigue in Vanadium dioxide

Vanadium dioxide is one of the most studied strongly correlated materials.
The nature of the rutile metal to monoclinic insulator transition in this system triggered a longstanding debate about which comes first, the Mott localisation or the Peierls distortion. Here, we show that the electronic correlations and the lattice vibrations conspire to stabilise the monoclinic insulator, and so they must be treated on equal footing. We design a minimal model for VO2 that includes all the important physical ingredients: the electronic correlations, the multi-orbital character, and the two components antiferrodistortive mode that condenses in the monoclinic insulator. We solve this model by dynamical mean-field theory within the adiabatic Born-Oppenheimer (BO) approximation. Consistently with the first-order character of the metal-insulator transition, the BO potential has a rich landscape describing the distorted and undistorted phases, and which translates into an equally rich thermodynamics that we uncover by the Monte Carlo method. Remarkably, we find that a distorted metal phase intrudes between the low-temperature distorted insulator and high-temperature undistorted metal, which sheds new light on the debated experimental evidence of a monoclinic metallic phase.