Predicting the temperature-strain phase diagram in VO₂

Predicting the phase diagram of VO$_2$, including the various structural allotopes, from first principles is a grand challenge of materials physics. The coexistence of Peierls and Mott physics suggests that a theory which can capture strong electronic correlations will be necessary to compute the total energies. Here we perform a detailed analysis of the structural energetics, and the electronic structure, of rutile and M$_1$ VO$_2$ using density functional theory (DFT) and DFT+U calculations. We demonstrate that there are qualitative failures in the structural energetics in both methods. In order to understand the nature of the failure, we build a minimal model of the structural energetics using the Peierls-Hubbard model and exactly solve it using DMRG (Density Matrix Renormalization Group); demonstrating that the on-site U has a minimal effect on the structural energetics for physical parameters. These results explain the partial success of the unorthodoxed non-spin-polarized (NSP) DFT+U results, and guide the creation of empirical corrections to the DFT+U functional. Our modified DFT+U functional is then used to predict the temperature-strain phase diagram for the rutile and M$_1$ phases.