A. A. Katanin

Dynamical vertex approximation — a step beyond dynamical mean field theory

Institute of Metal Physics, 620219 Ekaterinburg, Russia(Dated: Version 8, February 6, 2008)We develop a diagrammatic approach with local and nonlocal self-energy diagrams, constructedfrom the local irreducible vertex. This approach includes the local correlations of dynamical meanfield theory and long-range correlations beyond. It allows for example to describe (para-)magnonsand weak localization effects—in strongly correlated systems. As a first application, we study theinterplay between nonlocal antiferromagnetic correlations and the strong local correlations emergingin the vicinity of a Mott-Hubbard transition.

Self-consistent spin-wave theory of layered Heisenberg magnets

The versions of the self-consistent spin-wave theories (SSWT) of two-dimensional (2D) Heisenberg ferro- and antiferromagnets with a weak interlayer coupling and/or magnetic anisotropy, that are based on the non-linear Dyson-Maleev, Schwinger, and combined boson-pseudofermion representations, are analyzed. Analytical results for the temperature dependences of (sublattice) magnetization and short-range order parameter, and the critical points are obtained. The influence of external magnetic field is considered. Fluctuation corrections to SSWT are calculated within a random-phase approximation which takes into account correctly leading and next-leading logarithmic singularities. These corrections are demonstrated to improve radically the agreement with experimental data on layered perovskites and other systems. Thus an account of these fluctuations provides a quantitative theory of layered magnets.

Incommensurate magnetic order and phase separation in the two-dimensional Hubbard model with nearest- and next-nearest-neighbor hopping

We consider the ground-state magnetic phase diagram of the two-dimensional Hubbard model with nearest- and next-nearest-neighbor hopping in terms of electronic density and interaction strength. We treat commensurate ferromagnetic and antiferromagnetic as well as incommensurate (spiral) magnetic phases. The first-order magnetic transitions with changing chemical potential, resulting in a phase separation (PS) in terms of density, are found between ferromagnetic, antiferromagnetic, and spiral magnetic phases. We argue that PS has a dramatic influence on the phase diagram in the vicinity of half-filling. The results imply possible interpretation of the unusual behavior of magnetic properties of single-layer cuprates in terms of PS between collinear and spiral magnetic phases. The relevance of our results to the magnetic properties of the ruthenates is also discussed.

Fulfillment of Ward identities in the functional renormalization group approach

We consider the fulfillment of conservation laws and Ward identities in the one- and two-loop functional renormalization group approach. It is shown that in a one-particle irreducible scheme of this approach Ward identities are fulfilled only with the accuracy of the neglected two-loop terms

Comparing pertinent effects of antiferromagnetic fluctuations in the two and three dimensional Hubbard model

O({V}_{\ensuremath{\Lambda}}^{3})

Van Hove Singularity and Spontaneous Fermi Surface Symmetry Breaking in Sr3Ru2O7

at one-loop order, and with the accuracy

From Infinite to Two Dimensions through the Functional Renormalization Group

O({V}_{\ensuremath{\Lambda}}^{4})

Critical properties of the half-filled Hubbard model in three dimensions.

at two-loop order (

One-particle irreducible functional approach: A route to diagrammatic extensions of the dynamical mean-field theory

{V}_{\ensuremath{\Lambda}}

Dynamical Vertex Approximation An Introduction

is the effective interaction vertex at scale