# Unraveling the Mott-Peierls intrigue in Vanadium dioxide

## TL;DR

This paper investigates the complex interplay of electronic correlations and lattice effects in VO$_2$, proposing a comprehensive model solved with dynamical mean-field theory to clarify the metal-insulator transition and the existence of a monoclinic metallic phase.

## Contribution

It introduces a minimal model for VO$_2$ that includes key physical ingredients and solves it using dynamical mean-field theory, revealing new insights into the phase transition.

## Key findings

- Identification of a distorted metal phase between insulator and metal
- Rich thermodynamics with multiple minima in the Born-Oppenheimer potential
- Clarification of the monoclinic metallic phase evidence

## Abstract

Vanadium dioxide is one of the most studied strongly correlated materials. Nonetheless, the intertwining between electronic correlation and lattice effects has precluded a comprehensive description of the rutile metal to monoclinic insulator transition, in turn triggering a longstanding "the chicken or the egg" debate about which comes first, the Mott localisation or the Peierls distortion. Here, we suggest that this problem is in fact ill-posed: the electronic correlations and the lattice vibrations conspire to stabilise the monoclinic insulator, and so they must be both considered not to miss relevant pieces of the VO$_2$ physics. Specifically, we design a minimal model for VO$_2$ 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 approximation. Consistently with the first-order character of the metal-insulator transition, the Born-Oppenheimer potential has a rich landscape, with minima corresponding to the undistorted phase and to the four equivalent distorted ones, 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.