Cluster Dynamical Mean Field Theory of the Mott Transition

TL;DR

This paper investigates the Mott transition in the Hubbard model using cluster DMFT, showing that short-range correlations influence the transition's critical parameters and physical properties but do not change its first-order nature.

Contribution

It demonstrates that including short-range correlations in cluster DMFT modifies the phase diagram and physical characteristics without altering the transition's first-order nature.

Findings

Short-range correlations lower the critical U value.

The transition remains first order with cluster DMFT.

Anomalous metallic states with low coherence scale are observed.

Abstract

We address the nature of the Mott transition in the Hubbard model at half-filling using cluster Dynamical Mean Field Theory (DMFT). We compare cluster DMFT results with those of single site DMFT. We show that inclusion of the short range correlations on top of the on-site correlations, already treated exactly in single site DMFT, do not change the nature of the transition between the paramagnetic metal and the paramagnetic Mott insulator, which remains first order. However, the short range correlations reduce substantially the critical $U$ and modify the shape of transition lines. Moreover, they lead to very different physical properties of the metallic and insulating phases near the transition, in particular in the region of the phase diagram where the two solutions coexist. Approaching the transition from the metallic side, we find an anomalous metallic state with very low coherence scale at temperatures as low as $T=0.01t$. The insulating state is characterized by the relatively narrow Mott gap with pronounced peaks at the gap edge.