Pseudogaps: Introducing the Length Scale into DMFT

Pseudogap physics in strongly correlated systems is essentially scale dependent. We generalize the dynamical mean field theory (DMFT) by including into the DMFT equations dependence on correlation length of pseudogap fluctuations via additional (momentum dependent) self-energy Sigma_k. This self-energy describes non-local dynamical correlations induced by short-ranged collective SDW-like antiferromagnetic spin (or CDW-like charge) fluctuations. At high enough temperatures these fluctuations can be viewed as a quenched Gaussian random field with finite correlation length. This generalized DMFT+Sigma_k approach is used for the numerical solution of the weakly doped one-band Hubbard model with repulsive Coulomb interaction on a square lattice with nearest and next nearest neighbour hopping. The effective single impurity problem is solved by numerical renormalization group (NRG). Both types of strongly correlated metals, namely (i) doped Mott insulator and (ii) the case of bandwidth W<U (U - value of local Coulomb interaction) are considered. Densities of states, spectral functions and ARPES spectra calculated within DMFT+Sigma_k show a pseudogap formation near the Fermi level of the quasiparticle band. We also briefly discuss effects of random impurity scattering. Finally we demonstrate the qualitative picture of Fermi surface "destruction" due to pseudogap fluctuations and formation of "Fermi arcs" which agrees well with ARPES observations.