Extremely correlated Fermi liquid theory meets dynamical mean-field theory: Analytical insights into the doping-driven Mott transition

We consider a doped Mott insulator in the large dimensionality limit within both the recently developed extremely correlated Fermi liquid (ECFL) theory and the dynamical mean-field theory (DMFT). We show that the general structure of the ECFL sheds light on the rich frequency dependence of the DMFT self-energy. Using the leading Fermi liquid form of the two key auxiliary functions introduced in the ECFL theory, we obtain an analytical ansatz, which provides a good quantitative description of the DMFT self-energy down to hole doping level delta similar or equal to 0.2. In particular, the deviation from Fermi liquid behavior and the corresponding particle-hole asymmetry developing at a low-energy scale are well reproduced by this ansatz. The DMFT being exact at large dimensionality, our study also provides a benchmark of the ECFL in this limit. We find that the main features of the self-energy and spectral line shape are well reproduced by the ECFL calculations in the O(lambda(2)) minimal scheme, for not too low doping level delta greater than or similar to 0.3. The DMFT calculations reported here are performed using a state-of-the-art numerical renormalization-group impurity solver, which yields accurate results down to an unprecedentedly small doping level delta less than or similar to 0.001.