Pseudogaps: introducing the length scale into dynamical mean-field theory

Abstract

Pseudogap physics in strongly correlated systems is essentially scale dependent. We generalize the dynamical mean-field theory (DMFT) by introducing into the DMFT equations dependence on the correlation length of pseudogap fluctuations via an additional (momentum-dependent) self-energy S k . This self-energy describes nonlocal 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 + S 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 neighbor hopping. The effective single impurity problem is solved by the numerical renormalization group (NRG). Both types of strongly correlated metals, namely (i) the doped Mott insulator and (ii) the case of bandwidth W U (U is the value of local Coulomb interaction) are considered. Densities of states, spectral functions and ARPES spectra calculated within DMFT + S 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.

Generalized dynamical mean-field theory in the physics of strongly correlated systems

“…Finally, diagrammatic structure of the local self-energy remains identical to that of the standard DMFT and we obtain the following self-consistent equations of the generalized DMFT+Σ approach [23,24,25]:…”

“…phonons or spin fluctuations) are to be taken into account within some kind of perturbation theory, conserving, as far as possible, the general structure of DMFT equations. Actually, such a scheme can be realized in rather simple way [23,24,25].…”

“…Also in these approaches it is quite difficult to investigate two-particle properties. To overcome these difficulties we proposed recently [23,24,25] the new generalization of the conventional DMFT, allowing to consider non-local correlations or additional (with respect to the Hubbard one) interactions (in principle of any kind), remaining within a single impurity DFMT picture and preserving self-consistent set of DMFT equations.…”

DMFT+Σ approach to disordered hubbard model

“…Generalized DMFT+Σ approach [14][15][16][17] extends the standard DMFT [5][6][7] introducing an additional self-energy Σ p (ε) (in general case momentum dependent), which is due to some interaction mechanism outside the DMFT. It gives an effective procedure to calculate both single-and two-particle properties [18,21].…”

“…In recent years we have developed the so called generalized DMFT+Σ approach [14][15][16][17], which is very convenient for the studies of different additional interactions in repulsive Hubbard model, such as pseudogap fluctuations [14][15][16][17], disorder [18,19], electron -phonon interaction [20]) etc. This approach is also well suited to analyze twoparticle properties, such as optical (dynamic) conductivity [18,21].…”