arXiv subjects

A. A. Katanin

Publications and source records attributed to A. A. Katanin.

At least 73 records · Page 4Linked to original sources

arXiv2013

One-particle irreducible functional approach - a new route to diagrammatic extensions of DMFT

We present an approach which is based on the one-particle irreducible (1PI) generating functional formalism and includes electronic correlations on all length-scales beyond the local correlations of dynamical mean field theory (DMFT). This formalism allows us to unify aspects of the dynamical vertex approximation (D\GammaA) and the dual fermion (DF) scheme, yielding a consistent formulation of non-local correlations at the one- and two-particle level beyond DMFT within the functional integral formalism. In particular, the considered approach includes one-particle reducible contributions from the three- and more-particle vertices in the dual fermion approach, as well as some diagrams not included in the ladder version of D\GammaA. To demonstrate the applicability and physical content of the 1PI approach, we compare the diagrammatics of 1PI, DF and D\GammaA, as well as the numerical results of these approaches for the half-filled Hubbard model in two dimensions.

cond-mat.str-el↗

arXiv2013

Strong fluctuations near the frustration point in cubic lattice ferromagnets with localized moments

Thermodynamic properties of cubic Heisenberg ferromagnets with competing exchange interactions are considered near the frustration point where the coefficient $D$ in the spin-wave spectrum $E_{\mathbf{k}}\sim D k^{2}$ vanishes. Within the Dyson-Maleev formalism it is found that at low temperatures thermal fluctuations stabilize ferromagnetism by increasing the value of $D$. For not too strong frustration this leads to an unusual "concave" shape of the temperature dependence of magnetization, which is in agreement with experimental data on the europium chalcogenides. The phase diagram is constructed by means of Monte Carlo simulation, and suppression of magnetization and Curie temperature is found in comparison with the results of the spin-wave theory. This effect is explained by the the presence of non-analytical corrections to the spin-wave spectrum which are represented in the lowest order by the term $\sim (T/S)^{2} k^{2}\log{k}$.

cond-mat.str-el↗

arXiv2012

Magnetic fluctuations and itinerant ferromagnetism in two-dimensional systems with van Hove singularities

We use the quasistatic approach to analyze the criterion of ferromagnetism for two-dimensional (2D) systems with the Fermi level near Van Hove singularities (VHS) of the electronic spectrum. It is shown that the spectrum of spin excitations (paramagnons) is positively defined when the interaction I between electrons and paramagnons, which corresponds to the Hubbard on-site repulsion U, is sufficiently large. The critical interactions I_c and U_c remain finite at Van Hove filling and exceed considerably their values obtained from the Stoner criterion due to incommensurate spin fluctuations which are important near the ferromagnetic quantum phase transition. Combining the quasistatic approximation and the equation-of -motion method for the Green functions we obtain the results for the electronic self-energy to first order in the inverse number of spin components.

cond-mat.str-el↗

arXiv2011

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

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

cond-mat.str-el↗

arXiv2011

Ferromagnetism, spiral magnetic structures and phase separation in the two-dimensional Hubbard model

The quasistatic approximation and equation-of-motion decoupling for the electron Green's functions are applied to trace the effect of electronic dispersion and electron correlations on the ferromagnetism of two-dimensional itinerant-electron systems. It is found that next-nearest-neighbor hopping t' is of crucial importance for ferromagnetism formation yielding the magnetic phase diagram which is strongly asymmetric with respect to half-filling. At small t' in the vicinity of half-filling the ferromagnetic phase region is restricted by the spin-density wave instability, and far from half-filling by one-particle (spin-polaron) instability. At t' close to t/2 ferromagnetism is stabilized at moderate Hubbard U due to substantial curvature of the Fermi surface which passes in the vicinity of the van Hove singularity points. The results obtained are of possible importance for high-T_c compounds and layered ruthenates.

cond-mat.str-el↗

arXiv2011

Self-energy effects in the Polchinski and Wick-ordered renormalization-group approaches

I discuss functional renormalization group (fRG) schemes, which allow for non-perturbative treatment of the self-energy effects and do not rely on the one-particle irreducible functional. In particular, I consider Polchinski or Wick-ordered schemes with amputation of full (instead of bare) Green functions, as well as more general schemes, and eastablish their relation to the `dynamical adjustment propagator' scheme by M. Salmhofer [Ann. der Phys. 16, 171 (2007)]. While in the Polchinski scheme the amputation of full (instead of bare) Green functions improves treatment of the self-energy effects, the structure of the corresponding equations is not suitable to treat strong-coupling problems; it is not also evident, how the mean-field (MF) solution of these problems is recovered in this scheme. For Wick ordered scheme, excluding fully or partly tadpole diagrams one can obtain forms of fRG hierarchy, which are suitable to treat strong-coupling problems. In particular, I emphasize usefullness of the schemes, which are local in cutoff parameter, and compare them to the one-particle irreducible approach.

cond-mat.str-el↗

arXiv2011

Ab initio calculations with the dynamical vertex approximation

We propose an approach for the ab initio calculation of materials with strong electronic correlations which is based on all local (fully irreducible) vertex corrections beyond the bare Coulomb interaction. It includes the so-called GW and dynamical mean field theory and important non-local correlations beyond, with a computational effort estimated to be still manageable.

cond-mat.str-el↗

arXiv2011

The Neel temperature and sublattice magnetization for the stacked triangular-lattice antiferromagnet with a weak interlayer coupling

The quantum Heisenberg antiferromagnet on the stacked triangular lattice with the intralayer nearest-neighbor exchange interaction J and interlayer exchange J' is considered within the non-linear $σ$-model with the use of the renormalization group (RG) approach. For J' << J the asymptotic formula for the Neel temperature $T_{Neel}$ and sublattice magnetization are obtained. RG turns out to be insufficient to describe experimental data since it does not take into account the $\mathcal{Z}_2$-vortices. Therefore $T_{Neel}$ is estimated using the Monte-Carlo result for the 2D correlation length [10] which has a Kosterlitz-type behavior near the temperature $T_{KT}$ where the vortices are activated.

cond-mat.stat-mech↗

arXiv2011

Ferromagnetic instability and finite-temperature properties of two-dimensional electron systems with van Hove singularities

We study a ferromagnetic tendency in the two-dimensional Hubbard model near van Hove filling by using a functional renormalization-group method. We compute temperature dependences of magnetic susceptibilities including incommensurate magnetism. The ferromagnetic tendency is found to occur in a dome-shaped region around van Hove filling with an asymmetric property: incommensurate magnetism is favored near the edge of the dome above van Hove filling whereas a first-order-like transition to the ferromagnetic ground state is expected below van Hove filling. The dome-shaped phase diagram is well captured in the Stoner theory by invoking a smaller Coulomb interaction. Triplet p-wave superconductivity tends to develop at low temperatures inside the dome and extends more than the ferromagnetic region above van Hove filling.

cond-mat.str-el↗

arXiv2010

Magnetic fluctuations and self--energy effects in two--dimensional itinerant systems with van Hove singularity of electronic spectrum

We investigate a competition of tendencies towards ferromagnetic and incommensurate order in two-dimensional fermionic systems within functional renormalization group technique using temperature as a scale parameter. We assume that the Fermi surface (FS) is substantially curved, lies in the vicinity of van Hove singularity points and perform an account of the self-energy corrections. It is shown that the character of magnetic fluctuations is strongly asymmetric with respect to the Fermi level position relatively to van Hove singularity (VHS). For the Fermi level above VHS we find at low temperatures dominant incommensurate magnetic fluctuations, while below VHS level we find indications for ferromagnetic ground state. In agreement with the Mermin-Wagner theorem, at finite temperatures and in small magnetic fields we obtain rather small magnetization, which appears to be a power-law function of magnetic field. It is found that the FS curvature is slightly increased by correlation effects, and the renormalized bandwidth decreases at sufficiently low temperatures.

cond-mat.str-el↗

arXiv2010

Quasielastic neutron scattering from two dimensional antiferromagnets at a finite temperature

We consider frequency dependence of the neutron scattering amplitude from a two-dimensional quantum antiferromagnet. It is well known that the long range order disappears at any finite temperature and hence the elastic neutron scattering Bragg peak is transformed to the quasielastic neutron scattering spectrum ~dw/w. We show that the widely known formula for the spectrum of an isotropic antiferromagnet derived by Auerbach and Arovas should be supplemented by a logarithmic term that changes the integrated intensity by two times. A similar formula for an easy-plane magnet is very much different because of the Berezinsky-Kosterlitz-Thouless physics. An external uniform magnetic field switches smoothly the isotropic magnet to the easy-plane magnet. We demonstrate that the quasielastic neutron scattering spectrum in the crossover regime combines properties of both limiting cases. We also consider a quantum antiferromagnet close to the O(3) quantum critical point and show that in an external uniform magnetic field the intensity of elastic (quasielastic) neutron scattering peak depends linearly and significantly on the applied field.

cond-mat.str-el↗

arXiv2010

Linear-Temperature Dependence of Static Magnetic Susceptibility in LaFeAsO from Dynamical Mean-Field Theory

In this Letter we report the LDA+DMFT (method combining Local Density Approximation with Dynamical Mean-Field Theory) results for magnetic properties of parent superconductor LaFeAsO in paramagnetic phase. Calculated uniform magnetic susceptibility shows linear dependence at intermediate temperatures in agreement with experimental data. For high temperatures ($>$1000 K) calculations show saturation and then susceptibility decreases with temperature. Contributions to temperature dependence of the uniform susceptibility are strongly orbitally dependent. It is related to the form of the orbitally-resolved spectral functions near the Fermi energy with strong temperature dependent narrow peaks for some of the orbitals. Our results demonstrate that linear-temperature dependence of static magnetic susceptibility in pnictide superconductors can be reproduced without invoking antiferromagnetic fluctuations.

cond-mat.str-el↗

arXiv2009

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. We treat commensurate ferro- 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 the account of 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 one-layer cuprates in terms of PS between collinear and spiral magnetic phases. The relation of the results obtained to the magnetic properties of ruthenates is also discussed.

cond-mat.str-el↗

arXiv2009

Orbital selective local moment formation in iron: first principle route to an effective model

We revisit a problem of theoretical description of alpha-iron. By performing LDA+DMFT calculations in the paramagnetic phase we find that Coulomb interaction and, in particular Hund exchange, yields the formation of local moments in e_g electron band, which can be traced from imaginary time dependence of the spin-spin correlation function. This behavior is accompanied by non-Fermi-liquid behavior of e_g electrons and suggests using local moment variables in the effective model of iron. By investigating orbital-selective contributions to the Curie-Weiss law for Hund exchange I=0.9 eV we obtain an effective value of local moment of e_g electrons 2p=1.04 mu_B. The effective bosonic model, which allows to describe magnetic properties of iron near the magnetic phase transition, is proposed.

cond-mat.str-el↗

arXiv2009

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

We use the dynamical vertex approximation (D$Γ$A) with a Moriyaesque $% λ$ correction for studying the impact of antiferromagnetic fluctuations on the spectral function of the Hubbard model in two and three dimensions. Our results show the suppression of the quasiparticle weight in three dimensions and dramatically stronger impact of spin fluctuations in two dimensions where the pseudogap is formed at low enough temperatures. Even in the presence of the Hubbard subbands, the origin of the pseudogap at weak-to-intermediate coupling is in the splitting of the quasiparticle peak. At stronger coupling (closer to the insulating phase) the splitting of Hubbard subbands is expected instead. The $\mathbf{k}$-dependence of the self energy appears to be also much more pronounced in two dimensions as can be observed in the $\mathbf{k}$-resolved D$Γ$A spectra, experimentally accessible by angular resolved photoemission spectroscopy in layered correlated systems.

cond-mat.str-el↗

arXiv2008

Universal properties of frustrated spin systems: 1/N-expansion and renormalization group approaches

We consider a quantum two-dimensional O(N)xO(2)/O(N-2)xO(2) nonlinear sigma model for frustrated spin systems and formulate its 1/N-expansion which involves fluctuating scalar and vector fields describing kinematic and dynamic interactions, respectively. The ground state phase diagram of this model is obtained within the 1/N-expansion and 2+εrenormalization group approaches. The temperature dependence of correlation length in the renormalized classical and quantum critical regimes is discussed. In the region of the symmetry broken ground state ρ_in<ρ_out, χ_in<χ_out (rho_in,out and chi_in,out are the in- and out-of-plane spin stiffnesses and susceptibilities), where the mass M_μof the vector field can be arbitrarily small, physical properties at finite temperatures are universal functions of rho_in,out, chi_in,out, and temperature T. For small M_μthese properties show a crossover from low- to high temperature regime at T \sim M_μ. For ρ_in>ρ_out or χ_in>χ_out finite-temperature properties are universal functions only at sufficiently large M_μ. The high-energy behaviour in the latter regime is similar to the Landau-pole dependence of the physical charge e in quantum electrodynamics, with mass M_μplaying a role of e^{-1}. The application of the results obtained to the triangular-lattice Heisenberg antiferromagnet is considered.

cond-mat.str-el↗

arXiv2008

Strong short-range magnetic order in a frustrated FCC lattice and its possible role in the iron structural transformation

We investigate magnetic properties of a frustrated Heisenberg antiferromagnet with a face-centered cubic (FCC) lattice and exchange interactions between the nearest- and next-nearest neighbours, J1 and J2. In a collinear phase with the wave vector Q = (pi,pi,pi) the equations of the self-consistent spin-wave theory for the sublattice magnetization and the average short range order parameter are obtained and numerically solved. The dependence of the Neel temperature T_N on the ratio J2/J1 is obtained. It is shown, that at strong enough frustration there is a wide temperature region above T_N with strong short range magnetic order. Application of this result to description of structural phase transition between alpha and gamma-phase of Fe is considered.

cond-mat.str-el↗

arXiv2008

Spin fluctuations and ferromagnetic order in two-dimensional itinerant systems with Van Hove singularities

The quasistatic approach is used to analyze the criterion of ferromagnetism for two-dimensional (2D) systems with the Fermi level near Van Hove (VH) singularities of the electron spectrum. It is shown that the spectrum of spin excitations (paramagnons) is positively defined when the interaction between electrons and paramagnons, determined by the Hubbard on-site repulsion U, is sufficiently large. Due to incommensurate spin fluctuations near the ferromagnetic quantum phase transition, the critical interaction Uc remains finite at VH filling and exceeds considerably its value obtained from the Stoner criterion. A comparison with the functional renormalization group results and mean-field approximation which yields a phase separation is also performed.

cond-mat.str-el↗