**Физика Низких Температур: ***Том ***32**, Выпуск **4-5** (Апрель 2006), c. 528-537
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### Pseudogaps: introducing the length scale into dynamical mean-field theory

**E.Z. Kuchinskii, I.A. Nekrasov, and M.V. Sadovskii**

Institute for Electrophysics, Russian Academy of Sciences, Ekaterinburg, 620016, Russia

E-mail: sadovski@iep.uran.ru

*Received June 10, 2005*

**Аннотация**

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
Σ_{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 + Σ_{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 + Σ_{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.

**PACS:**

71.10.Fd - Lattice fermion models (Hubbard model, etc.)

71.10.Hf - Non-Fermi-liquid ground states, electron phase diagrams and phase transitions in model systems

71.27.+a - Strongly correlated electron systems; heavy fermions

71.30.+h - Metal-insulator transitions and other electronic transitions

74.72.-h - Cuprate superconductors (high-Tc and insulating parent compounds)

**Ключевые слова: **pseudogap, strongly correlated systems, spin fluctuations.