Study of the dimer Hubbard Model within Dynamical Mean Field Theory and its application to VO$_2$

Abstract

We study in detail the solution of a basic strongly correlated model,namely, the dimer Hubbard model. This model is the simplest realization ofa cluster DMFT problem.We provide a detailed description of the solutions in the “coexistent region” where two (meta)stable states of the DMFT equations are found, onea metal and the other an insulator. Moreover, we describe in detail howthese states break down at their respective critical lines. We clarify thekey role played by the intra-dimer correlation, which here acts in additionto the onsite Coulomb correlations.We review the important issue of the Mott-Peierls insulator crossoverwhere we characterize a variety of physical regimes. In a subtle change inthe electronic structure the Hubbard bands evolve from purely incoherent(Mott) to purely coherent (Peierls) through a state with unexpected mixedcharacter. We find a singlet pairing temperature T* below which thelocalized electrons at each atomic site can bind into a singlet and quenchtheir entropy, this uncovers a new paradigm of a para-magnetic Mottinsulator.Finally, we discuss the relevance of our results for the interpretation ofvarious experimental studies in VO\(_2\). We present a variety of argumentsthat allow us to advance the conclusion that the long-lived (meta-stable)metallic phase, induced in pump-probe experiments, and the thermallyactivated M\(_1\) meta-stable metallic state in nano-domains are the same. In fact, they may all be qualitatively described by the dimerizedcorrelated metal state of our model.