Computation of the Correlated Metal-Insulator Transition in Vanadium Dioxide from First Principles

Vanadium dioxide (${\mathrm{VO}}_2$) is a paradigmatic example of a strongly correlated system that undergoes a metal-insulator transition at a structural phase transition. To date, this transition has necessitated significant post hoc adjustments to theory in order to be described properly. Here we report standard state-of-the-art first principles quantum Monte Carlo (QMC) calculations of the structural dependence of the properties of ${\mathrm{VO}}_2$. Using this technique, we simulate the interactions between electrons explicitly, which allows for the metal-insulator transition to naturally emerge, importantly without ad hoc adjustments. The QMC calculations show that the structural transition directly causes the metal-insulator transition and a change in the coupling of vanadium spins. This change in the spin coupling results in a prediction of a momentum-independent magnetic excitation in the insulating state. While two-body correlations are important to set the stage for this transition, they do not change significantly when ${\mathrm{VO}}_2$ becomes an insulator. These results show that it is now possible to account for electron correlations in a quantitatively accurate way that is also specific to materials.

Figure 1

FN-DMC energies of ${\mathrm{VO}}_2$ with trial wave functions from DFT of different hybrid functionals. All the energies are relative to the monoclinic AFM state: $-2830.836(2)\mathrm{eV}$.

Figure 2

FN-DMC energetic results: (a) per ${\mathrm{VO}}_2$ unit for different magnetically ordered states, spin-unpolarized, ferromagnetic (FM), and antiferromagnetic [AFM and AFM (intra)]. Energies are relative to the monoclinic AFM state. (b) Optical gaps for various states. (c) Spin density for various states.

Figure 3

Temperature dependence of magnetic susceptibility obtained by Ising model simulation on a ${\mathrm{VO}}_2$ lattice, with magnetic coupling from FN-DMC compared to results from Zylbersztejn [6] and Kosuge [30]. There has been an overall scale applied on the data, and the transition temperature is indicated by the vertical dashed line.

Figure 4

Change of V-O hybridizations manifested through: (a) Intersite charge ($n_i$), and unlike-spin ($n_{i\uparrow }$ or $n_{i\downarrow }$) covariance quantified as $⟨O_i{O}_j⟩-⟨O_i⟩⟨O_j⟩$, where $O_i$ is the onsite value of specific physical quantities. The intersite covariance between a chosen vanadium center and the surrounding atoms is plotted as a function of the interatomic distance. (b) Onsite spin-resolved probability distribution on vanadium atoms—$\rho (n_i^{\uparrow },n_i^{\downarrow })$. (c) Spin and charge density of the rutile and monoclinic ${\mathrm{VO}}_2$. Figures on the left panel are 3D isosurface plots of spin density, and on the right panel are contour plots of spin and charge density on the [110] plane.