The inclusion of strong electronic correlations into a theoretical description solids is notoriously hard problem. This review describes various recent schemes to improve on dynamical mean field theory, which includes only local correlations, by systematically incorporating nonlocal as well, and discusses applications standard models strongly correlated electrons.

We develop a diagrammatic approach with local and nonlocal self-energy diagrams, constructed from the irreducible vertex. This includes correlations of dynamical mean field theory long-range beyond. It allows for example to describe (para-)magnons weak localization effects in strongly correlated systems. As first application, we study interplay between antiferromagnetic strong emerging vicinity Mott-Hubbard transition.

We use the dynamical vertex approximation (D$\Gamma$A) with a Moriyaesque $% \lambda$ correction for studying impact of antiferromagnetic fluctuations on spectral function Hubbard model in two and three dimensions. Our results show suppression quasiparticle weight dimensions dramatically stronger spin where pseudogap is formed at low enough temperatures. Even presence subbands, origin weak-to-intermediate coupling splitting peak. At (closer to insulating phase) subbands expected instead. The...

We present a novel scheme for an unbiased, nonperturbative treatment of strongly correlated fermions. The proposed approach combines two the most successful many-body methods, dynamical mean field theory and functional renormalization group. Physically, this allows systematic inclusion nonlocal correlations via group flow equations, after local are taken into account nonperturbatively by theory. To demonstrate feasibility approach, we numerical results two-dimensional Hubbard model at half filling.

Abstract Some Bravais lattices have a particular geometry that can slow down the motion of Bloch electrons by pre-localization due to band-structure properties. Another known source electronic localization in solids is Coulomb repulsion partially filled d or f orbitals, which leads formation local magnetic moments. The combination these two effects usually considered little relevance strongly correlated materials. Here we show it represents, instead, underlying physical mechanism most...

We consider the fulfillment of conservation laws and Ward identities in one- two-loop functional renormalization group approach. It is shown that a one-particle irreducible scheme this approach are fulfilled only with accuracy neglected terms $O({V}_{\ensuremath{\Lambda}}^{3})$ at one-loop order, $O({V}_{\ensuremath{\Lambda}}^{4})$ order (${V}_{\ensuremath{\Lambda}}$ effective interaction vertex scale $\ensuremath{\Lambda}$). The self-consistent version equations which leads to smaller...

We consider the ground-state magnetic phase diagram of two-dimensional Hubbard model with nearest- and next-nearest-neighbor hopping in terms electronic density interaction strength. treat commensurate ferromagnetic antiferromagnetic as well incommensurate (spiral) phases. The first-order transitions changing chemical potential, resulting a separation (PS) density, are found between ferromagnetic, antiferromagnetic, spiral argue that PS has dramatic influence on vicinity half-filling....

By means of the dynamical vertex approximation (D$\Gamma$A) we include spatial correlations on all length scales beyond mean field theory (DMFT) for half-filled Hubbard model in three dimensions. The most relevant changes due to non-local fluctuations are: (i) a deviation from mean-field critical behavior with same exponents as dimensional Heisenberg (anti)-ferromagnet and (ii) sizable reduction N\'eel temperature ($T_N$) by $\sim 30%$ onset antiferromagnetic order. Finally, give...

We present an approach which is based on the one-particle irreducible (1PI) generating functional formalism and includes electronic correlations all length scales beyond local of dynamical mean-field theory (DMFT). This allows us to unify aspects vertex approximation (D$\ensuremath{\Gamma}$A) dual fermion (DF) scheme, yielding a consistent formulation nonlocal at one- two-particle level DMFT within integral formalism. In particular, considered reducible contributions from three-...

The versions of the self-consistent spin-wave theories (SSWT) two-dimensional Heisenberg ferro- and antiferromagnets with a weak interlayer coupling and/or magnetic anisotropy, that are based on nonlinear Dyson-Maleev, Schwinger, combined boson-pseudofermion representations, analyzed. Analytical results for temperature dependences (sublattice) magnetization short-range order parameter, critical points obtained. influence external field is considered. Fluctuation corrections to SSWT...

The pinning of the Fermi level to Van Hove singularity and formation flat bands in two-dimensional t-t' Hubbard model is investigated by renormalization group technique. "Van Hove" scenario non-Fermi-liquid behavior for high-T(c) compounds can take place a broad enough range hole concentrations. results are qualitative agreement with recent angle-resolved photoemission spectroscopy data on La 2CuO (4).

We revisit a problem of theoretical description alpha-iron. By performing LDA+DMFT calculations in the paramagnetic phase we find that Coulomb interaction and, particular Hund exchange, yields formation local moments e_g electron band, which can be traced from imaginary time dependence spin-spin correlation function. This behavior is accompanied by non-Fermi-liquid electrons and suggests using moment variables effective model iron. investigating orbital-selective contributions to Curie-Weiss...

We propose an efficient dual boson scheme, which extends the DMFT paradigm to collective excitations in correlated systems. The theory is fully self-consistent both on one- and two-particle level, thus describing formation of modes as well renormalization electronic bosonic spectra equal footing. method employs effective impurity model comprising fermionic hybridization functions. Only single- two-electron Green's functions reference problem enter theory, due optimal choice self-consistency...

A general understanding of quantum phase transitions in strongly correlated materials is still lacking. By exploiting a cutting-edge many-body approach, the dynamical vertex approximation, we make an important progress, determining critical properties antiferromagnetic transition fundamental model for electrons, Hubbard three dimensions. In particular, demonstrate that -in contradiction to conventional Hertz-Millis-Moriya theory- its behavior driven by Kohn anomalies Fermi surface, even when...

Strong repulsive interactions between electrons can lead to a Mott metal-insulator transition. The Dynamical Mean-Field Theory (DMFT) explains the critical end-point and hysteresis region with single-particle concepts such as spectral function quasiparticle weight. In this work, we reconsider end point of transition on two-particle level. We show that relevant eigenvalue eigenvector non-local Bethe-Salpeter kernel provide unified picture particular, they simultaneously explain thermodynamics...

The t-t' Hubbard model for the Fermi level near Van Hove singularity is considered within renormalization group and parquet approaches. interplay of ferromagnetic, antiferromagnetic, superconducting channels investigated, phase diagram constructed. In comparison with previous approaches, account ferromagnetic fluctuations suppresses pairing and, vice versa, influence Cooper channel decreases Curie temperature, so that Stoner criterion inapplicable even qualitatively.

Phase diagrams of the two-dimensional one-band $t\ensuremath{-}{t}^{\ensuremath{'}}$ Hubbard model are obtained within two-patch and temperature-cutoff many-patch renormalization group approaches. At small ${t}^{\ensuremath{'}}$ at van Hove band fillings antiferromagnetism dominates, while with increasing or changing filling is replaced by d-wave superconductivity. Near ${t}^{\ensuremath{'}}=t/2$ close to system unstable towards ferromagnetism. Away from this ferromagnetic instability a...

Using the one-loop functional renormalization group technique we evaluate self-energy in weak-coupling regime of 2D t-t' Hubbard model. At van Hove (vH) band fillings and at low temperatures quasiparticle weight along Fermi surface (FS) continuously vanishes on approaching (pi,0) point where concept is invalid. Away from vH peak formed inside an anisotropic pseudogap has conventional Fermi-liquid characteristics near level. The spectral features reduced parts FS between vicinity hot spots...

We give an elementary introduction to a recent diagrammatic extension of dynamical mean field theory (DMFT) coined vertex approximation (DΓA). This approach contains the important local correlations DMFT, giving, among others, rise quasiparticle renormalizations, Mott-Hubbard transitions and magnetism, but also non-local beyond. The latter are at very essence many physical phenomena in strongly correlated elecectron systems. As treated equally on all length scales, DΓA allows us describe...

We present a general frame to extend functional renormalization group (fRG) based computational schemes by using an exactly solvable interacting reference problem as starting point for the RG flow. The systematic expansion around this solution accounts nonperturbative inclusion of correlations. Introducing auxiliary fermionic fields means Hubbard-Stratonovich transformation, we derive flow equations and determine relation conventional weak-coupling truncation hierarchy equations. As specific...

We investigate magnetic properties of CrTe2 within the density functional theory (DFT) approach in ferromagnetic phase and combination DFT dynamical mean field (DFT+DMFT) paramagnetic phase. show that a few-layer possesses well-formed local moments. In monolayer CrTe2, we find most preferable antiferromagnetic exchange with 120∘ structure. bilayer trilayer systems, electronic correlations DFT+DMFT yield interaction each layer, but between layers is antiferromagnetic, such alternation...

We consider the square lattice Heisenberg antiferromagnet with plaquette ring exchange and a finite interlayer coupling leading to consistent description of spin-wave excitation spectrum in La2CuO4. The values in-plane parameters, including ring-exchange J_{\Box}, are obtained consistently by an accurate fit experimentally observed dispersion, while out-of-plane interaction is found from temperature dependence sublattice magnetization at low temperatures. fitted interactions J=151.9 meV...

Applying the local density and dynamical mean field approximations to paramagnetic \gamma-iron we revisit problem of theoretical description magnetic properties in a wide temperature range. We show that contrary \alpha-iron, frequency dependence electronic self-energy has quasiparticle form for both, t_{2g} e_g states. In range T=1200-1500 K, where exist nature, this substance can be nevertheless characterized by temperature-dependent effective moments, which yield relatively narrow peaks...

We study the phase diagram and quantum critical region of one fundamental models for electronic correlations: periodic Anderson model. Employing recently developed dynamical vertex approximation, we find a transition between zero-temperature antiferromagnetic insulator Kondo insulator. In region, determine exponent $\ensuremath{\gamma}=2$ susceptibility. At higher temperatures, have free spins with $\ensuremath{\gamma}=1$ instead, whereas at lower there is an even stronger increase...

We study the formation of local magnetic moments in strongly correlated Hubbard model within dynamical mean-field theory and associate peculiarities temperature dependence charge ${\ensuremath{\chi}}_{c}$ spin ${\ensuremath{\chi}}_{s}$ susceptibilities with different stages moment formation. The maximum susceptibility is associated beginning formation, while minimum double occupation, as well low-temperature boundary plateau effective...