A. N. Rubtsov

Publications (41)34.06 Total impact

• Article: Role of rotational symmetry in the magnetism of a multiorbital model

  A. E. Antipov, I. S. Krivenko, V. I. Anisimov, A. I. Lichtenstein, A. N. Rubtsov
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  ABSTRACT: Effect of rotationally-invariant Hund's rule coupling on a magnetism of multiorbital Hubbard models is studied within a dynamical mean field theory framework. Comparison of static magnetic susceptibilities and local densities of states of two- and three-orbital models of a complete rotationally invariant Coulomb interaction and a "density-density" Hartree type interaction shows the different role of spin-flip interactions for different band fillings. In the particle-hole symmetric case the Mott-Hubbard physics dominates due to the strong effective Coulomb interaction, while for the multiple electronic configurations away from half-filling (two electrons in the three band model) the formation of local magnetic moments due to Hund's exchange interaction becomes the most significant effect for itinerant magnetic systems. A shift of the temperature of magnetic ordering due to the rotationally-invariant Hund's rule coupling is found to be the largest in a three-orbital model with a two-electron occupancy where the single particle spectrum is metallic and is not sensitive to different forms of the Coulomb vertex. A larger enhancement of the effective mass in a model with a rotationally-invariant interaction is discussed. In the half-filled case we find a drastic change in the density of states close to the Mott transition which is related to the spin-flip Kondo fluctuations in a degenerate orbital case, while the corresponding shift of the magnetic transition temperature is relatively small. It is shown that a change in the ground state degeneracy due to a different symmetry of the Coulomb interaction in the density-density model leads to a breakdown of the quasiparticle peak at the Fermi level in the proximity of a Mott transition on the metallic side. We discuss the relevance of rotationally-invariant Hund's interaction in the transition metal magnetism.
  Physical Review B 06/2012; 86:155107. · 3.69 Impact Factor
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  Available from: Mikhail I. Katsnelson

  Article: Dual boson approach to collective excitations in correlated fermionic systems

  A. N. Rubtsov, M. I. Katsnelson, A. I. Lichtenstein
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  ABSTRACT: We develop a general theory of a boson decomposition for both local and non-local interactions in lattice fermion models which allows us to describe fermionic degrees of freedom and collective charge and spin excitations on equal footing. An efficient perturbation theory in the interaction of the fermionic and the bosonic degrees of freedom is constructed in so-called dual variables in the path-integral formalism. This theory takes into account all local correlations of fermions and collective bosonic modes and interpolates between itinerant and localized regimes of electrons in solids. The zero-order approximation of this theory corresponds to extended dynamical mean-field theory (EDMFT), a regular way to calculate nonlocal corrections to EDMFT is provided. It is shown that dual ladder summation gives a conserving approximation beyond EDMFT. The method is especially suitable for consideration of collective magnetic and charge excitations and allows to calculate their renormalization with respect to "bare" RPA-like characteristics. General expression for the plasmonic dispersion in correlated media is obtained. As an illustration it is shown that effective superexchange interactions in the half-filled Hubbard model can be derived within the dual-ladder approximation.
  05/2011;
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  Available from: Mikhail I. Katsnelson

  Article: Dual-Fermion approach to Non-equilibrium strongly correlated problems

  C. Jung, A. Lieder, S. Brener, H. Hafermann, B. Baxevanis, A. Chudnovskiy, A. N. Rubtsov, M. I. Katsnelson, A. I. Lichtenstein
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  ABSTRACT: We present a generalization of the recently developed dual fermion approach introduced for correlated lattices to non-equilibrium problems. In its local limit, the approach has been used to devise an efficient impurity solver, the superperturbation solver for the Anderson impurity model (AIM). Here we show that the general dual perturbation theory can be formulated on the Keldysh contour. Starting from a reference Hamiltonian system, in which the time-dependent solution is found by exact diagonalization, we make a dual perturbation expansion in order to account for the relaxation effects from the fermionic bath. Simple test results for closed as well as open quantum systems in a fermionic bath are presented. Comment: 21 pages, 6 figures
  11/2010;
• Article: Importance of full Coulomb interactions for understanding the electronic structure of δ-Pu

  E. Gorelov, J. Kolorenč, T. Wehling, H. Hafermann, A. B. Shick, A. N. Rubtsov, A. Landa, A. K. McMahan, V. I. Anisimov, M. I. Katsnelson, A. I. Lichtenstein
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  ABSTRACT: Understanding the electronic structure of materials containing elements from the end of the periodic table represents a challenge due to a complex interplay of a number of physical phenomena occurring in these systems. In the plutonium metal, a fraction of the valence electrons is at the turning point between joining the conduction cloud, which occupies the whole crystal, and staying bound to a particular atom. This delicate boundary can be probed by photoemission experiments. Here we employ a very accurate computational method—the quantum Monte Carlo simulations—to describe the electronic states in the material achieving previously inaccessible resolution. We show that in order to successfully analyze the experimental photoemission spectra, it is essential to include the complete form of the electron-electron interaction into the Schrödinger equation, otherwise the spectral features near the Fermi level are not correctly reproduced.
  Phys. Rev. B. 08/2010; 82(8).
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  Available from: Mikhail I. Katsnelson

  Article: Electron energy spectrum of the spin-liquid state in a frustratedHubbard model

  A. E. Antipov, A. N. Rubtsov, M. I. Katsnelson, A. I. Lichtenstein
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  ABSTRACT: Non-local correlation effects in the half-filled Hubbard model on an isotropic triangular lattice are studied within a spin polarized extension of the dual fermion approach. A competition between the antiferromagnetic non-collinear and the spin liquid states is strongly enhanced by an incorporation of a k-dependent self-energy beyond the local dynamical mean-field theory. The dual fermion correc- tions drastically decrease the energy of a spin liquid state while leaving the non-collinear magnetic states almost non-affected. This makes the spin liquid to become a preferable state in a certain interval of interaction strength of an order of the magnitude of a bandwidth. The spectral function of the spin-liquid Mott insulator is determined by a formation of local singlets which results in the energy gap of about twice larger than that of the 120 degrees antiferromagnetic Neel state.
  Physical Review B 06/2010; 83(11):115126. · 3.69 Impact Factor
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  Available from: Mikhail I. Katsnelson

  Article: Analytical approximation for single-impurity Anderson model

  I. S. Krivenko, A. N. Rubtsov, M. I. Katsnelson, A. I. Lichtenstein
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  ABSTRACT: We have applied the recently developed dual fermion technique to the spectral properties of single-band Anderson impurity problem (SIAM). In our approach a series expansion is constructed in vertices of the corresponding atomic Hamiltonian problem. This expansion contains a small parameter in two limiting cases: in the weak coupling case ($U/t \to 0$), due to the smallness of the irreducible vertices, and near the atomic limit ($U/t \to \infty$), when bare propagators are small. Reasonable results are obtained also for the most interesting case of strong correlations ($U \approx t$). The atomic problem of the Anderson impurity model has a degenerate ground state, so the application of the perturbation theory is not straightforward. We construct a special approach dealing with symmetry-broken ground state of the renormalized atomic problem. Formulae for the first-order dual diagram correction are obtained analytically in the real-time domain. Most of the Kondo-physics is reproduced: logarithmic contributions to the self energy arise, Kondo-like peak at the Fermi level appears, and the Friedel sum rule is fulfilled. Our approach describes also renormalization of atomic resonances due to hybridization with a conduction band. A generalization of the proposed scheme to a multi-orbital case can be important for the realistic description of correlated solids. Comment: 6 pages, 5 figures
  10/2009;
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  Available from: Mikhail I. Katsnelson

  Article: Efficient perturbation theory for quantum lattice models.

  H Hafermann, G Li, A N Rubtsov, M I Katsnelson, A I Lichtenstein, H Monien
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  ABSTRACT: We present a novel approach to long-range correlations beyond dynamical mean-field theory, through a ladder approximation to dual fermions. The new technique is applied to the two-dimensional Hubbard model. We demonstrate that the transformed perturbation series for the nonlocal dual fermions has superior convergence properties over standard diagrammatic techniques. The critical Néel temperature of the mean-field solution is suppressed in the ladder approximation, in accordance with quantum Monte Carlo results. An illustration of how the approach captures and allows us to distinguish short- and long-range correlations is given.
  Physical Review Letters 06/2009; 102(20):206401. · 7.37 Impact Factor
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  Available from: Mikhail I. Katsnelson

  Article: Relevance of complete Coulomb interaction matrix for the Kondo problem: Co impurity on Cu(111)

  E. Gorelov, T. O. Wehling, A. N. Rubtsov, M. I. Katsnelson, A. I. Lichtenstein
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  ABSTRACT: The electronic structure of a prototype Kondo system, a cobalt impurity in a copper host is calculated with accurate taking into account of correlation effects on the Co atom. Using the recently developed continuous-time QMC technique, it is possible to describe the Kondo resonance with a complete four-index Coulomb interaction matrix. This opens a way for completely first-principle calculations of the Kondo temperature. We have demonstrated that a standard practice of using a truncated Hubbard Hamiltonian to consider the Kondo physics can be quantitatively inadequate. Comment: 6 pages, 4 figures
  05/2009;
• Article: Understanding the electronic structure and magnetism of correlated nanosystems.

  H Hafermann, S Brener, A N Rubtsov, M I Katsnelson, A I Lichtenstein
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  ABSTRACT: In this paper we review recent developments towards a realistic description of the electronic structure and magnetism of correlated nanosystems. A new class of so-called continuous-time solvers for the quantum impurity problem is discussed, which provides a numerically exact solution without systematic errors due to imaginary time discretization. These solvers are able to handle general interactions, like the full Coulomb vertex. We further show how four-point or higher-order correlation functions of the impurity problem can be computed. This allows the calculation of dynamical susceptibilities which provide information about spin excitations. Moreover, we discuss a principally new many-body scheme recently proposed for the description of non-local correlations in strongly correlated systems. This approach provides a basis for a many-body description of extended correlated nanostructures on a substrate.
  Journal of Physics Condensed Matter 02/2009; 21(6):064248. · 2.55 Impact Factor
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  Available from: Mikhail I. Katsnelson

  Article: Superperturbation solver for quantum impurity models

  H. Hafermann, C. Jung, S. Brener, M. I. Katsnelson, A. N. Rubtsov, A. I. Lichtenstein
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  ABSTRACT: We present a very efficient solver for the general Anderson impurity problem. It is based on the perturbation around a solution obtained from exact diagonalization, using a small number of bath sites. We formulate a perturbation theory which is valid for both weak and strong coupling and interpolates between these limits. Good agreement with numerically exact quantum Monte Carlo results is found for a single bath site over a wide range of parameters. In particular, the Kondo resonance in the intermediate-coupling regime is well reproduced for a single bath site and the lowest-order correction. The method is particularly suited for low temperatures, alleviates analytical continuation of imaginary time data due to the absence of statistical noise and can be generalized to obtain dynamical quantities directly on the real axis.
  EPL (Europhysics Letters) 01/2009; 85(2):27007. · 2.17 Impact Factor
• Article: Dual Fermion Approach to High-Temperature Superconductivity

  H. Hafermann, M. Kecker, S. Brener, A. N. Rubtsov, M. I. Katsnelson, A. I. Lichtenstein
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  ABSTRACT: We present an extension of the recently proposed dual fermion approach to investigate the superconducting properties of the Hubbard model in two dimensions. From the spin–spin susceptibility, we find a reduction of the Néel temperature compared to results from dynamical mean-field theory (DMFT) calculations due to the incorporation of spatial correlations. We present results for the temperature dependence of the leading eigenvalue of the Bethe–Salpeter equation for the particle–particle channel. In agreement with previous studies, we find singlet d-wave pairing to be the dominant contribution to pairing. We further present first results for the finite-doping phase diagram obtained from the leading eigenvalue of the Bethe–Salpeter equations for the particle–hole and particle–particle channels.
  Journal of Superconductivity and Novel Magnetism 12/2008; 22(1):45-49. · 0.65 Impact Factor
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  Available from: Mikhail I. Katsnelson

  Article: Dual fermion approach to the two-dimensional Hubbard model: Antiferromagnetic fluctuations and Fermi arcs

  A. N. Rubtsov, M. I. Katsnelson, A. I. Lichtenstein, A. Georges
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  ABSTRACT: We present an efficient diagrammatic method to describe nonlocal correlation effects in lattice fermion Hubbard-like models, which is based on a change of variables in the Grassmann path integrals. The new fermions are dual to the original ones and correspond to weakly interacting quasiparticles in the case of strong local correlations in the Hubbard model. The method starts with dynamical mean-field theory as a zeroth-order approximation and includes non-local effects in a perturbative way. In contrast to cluster approaches, this method utilizes an exact transition to a dual set of variables. It therefore becomes possible to treat the irreducible vertices of an effective {\it single-impurity} problem as small parameters. This provides a very efficient interpolation between band-like weak-coupling and atomic limits. The method is illustrated on the two-dimensional Hubbard model. The antiferromagnetic pseudogap, Fermi-arc formations, and non-Fermi-liquid effects due to the van Hove singularity are correctly reproduced by the lowest-order diagrams. Extremum properties of the dual fermion approach are discussed in terms of the Feynman variational principle. Comment: 15 pages, 15 figures Second version + minor changes
  10/2008;
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  Available from: Mikhail I. Katsnelson

  Article: Dual Fermion Approach to Susceptibility of Correlated Lattice Fermions

  S. Brener, H. Hafermann, A. N. Rubtsov, M. I. Katsnelson, A. I. Lichtenstein
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  ABSTRACT: In this paper, we show how the two-particle Green function (2PGF) can be obtained within the framework of the Dual Fermion approach. This facilitates the calculation of the susceptibility in strongly correlated systems where long-ranged non-local correlations cannot be neglected. We formulate the Bethe-Salpeter equations for the full vertex in the particle-particle and particle-hole channels and introduce an approximation for practical calculations. The scheme is applied to the two-dimensional Hubbard model at half filling. The spin-spin susceptibility is found to strongly increase for the wavevector $\vc{q}=(\pi,\pi)$, indicating the antiferromagnetic instability. We find a suppression of the critical temperature compared to the mean-field result due to the incorporation of the non-local spin-fluctuations. Comment: 10 pages, 5 figures; substantially extended results section compared to version 1
  11/2007;
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  Available from: Mikhail I. Katsnelson

  Article: Cluster Dual Fermion Approach to Nonlocal Correlations

  H. Hafermann, S. Brener, A. N. Rubtsov, M. I. Katsnelson, A. I. Lichtenstein
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  ABSTRACT: We formulate a general cluster Dual Fermion Approach to nonlocal correlations in crystals. The scheme allows the treatment of long-range correlations beyond cluster DMFT and nonlocal effects in realistic calculations of multiorbital systems. We show that the the simplest approximation exactly corresponds to free cluster DMFT. We further consider the relation between the two-particle Green functions in real and dual variables. We apply this approach by calculating the Green function of the Hubbard model in one dimension starting from the two-site cluster DMFT solution. The result agrees well with the Green function obtained from a DMRG calculation.
  07/2007;
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  Available from: ArXiv

  Article: Energy diffusion in strongly driven quantum chaotic systems: Role of correlations of the matrix elements

  P. V. Elyutin, A. N. Rubtsov
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  ABSTRACT: The energy evolution of a quantum chaotic system under the perturbation that harmonically depends on time is studied for the case of large perturbation, in which the rate of transition calculated from the Fermi golden rule (FGR) is about or exceeds the frequency of perturbation. For this case the models of Hamiltonian with random non-correlated matrix elements demonstrate that the energy evolution retains its diffusive character, but the rate of diffusion increases slower than the square of the magnitude of perturbation, thus destroying the quantum-classical correspondence for the energy diffusion and the energy absorption in the classical limit $\hbar \to 0$. The numerical calculation carried out for a model built from the first principles (the quantum analog of the Pullen - Edmonds oscillator) demonstrates that the evolving energy distribution, apart from the diffusive component, contains a ballistic one with the energy dispersion that is proportional to the square of time. This component originates from the chains of matrix elements with correlated signs and vanishes if the signs of matrix elements are randomized. The presence of the ballistic component formally extends the applicability of the FGR to the non-perturbative domain and restores the quantum-classical correspondence.
  01/2007;
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  Available from: Tanusri Saha-Dasgupta

  Article: Enhanced Crystal Field Splitting and Orbital Selective Coherence by Strong Correlations in V_2O_3

  A. I. Poteryaev, J. M. Tomczak, S. Biermann, A. Georges, A. I. Lichtenstein, A. N. Rubtsov, T. Saha-Dasgupta, O. K. Andersen
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  ABSTRACT: We present a study of the paramagnetic metallic and insulating phases of vanadium sesquioxide by means of the $N$th order muffin-tin orbital implementation of density functional theory combined with dynamical mean-field theory. The transition is shown to be driven by a correlation-induced enhancement of the crystal field splitting within the $t_{2g}$ manifold, which results in a suppression of the hybridization between the $a_{1g}$ and $e_g^{\pi}$ bands. We discuss the changes in the effective quasi-particle band structure caused by the correlations and the corresponding self-energies. At temperatures of about 400 K we find the $a_{1g}$ orbitals to display coherent quasi-particle behavior, while a large imaginary part of the self-energy and broad features in the spectral function indicate that the $e_g^{\pi}$ orbitals are still far above their coherence temperature. The local spectral functions are in excellent agreement with recent bulk sensitive photoemission data. Finally, we also make a prediction for angle-resolved photoemission experiments by calculating momentum-resolved spectral functions. Comment: Paper I will appear in condmat in two weeks
  01/2007;
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  Available from: Mikhail I. Katsnelson

  Article: Dual fermion approach to nonlocal correlations in the Hubbard model

  A. N. Rubtsov, M. I. Katsnelson, A. I. Lichtenstein
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  ABSTRACT: A new diagrammatic technique is developed to describe nonlocal effects (e.g., pseudogap formation) in the Hubbard-like models. In contrast to cluster approaches, this method utilizes an exact transition to the dual set of variables, and it therefore becomes possible to treat the irreducible vertices of an effective {\it single-impurity} problem as small parameters. This provides a very efficient interpolation between weak-coupling (band) and atomic limits. The antiferromagnetic pseudogap formation in the Hubbard model is correctly reproduced by just the lowest-order diagrams.
  01/2007;
• Article: Numerical study of the paraelectric-incommensurate- ferroelectric transition in the DIFFOUR model

  A. N. Rubtsov, T. Janssen
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  ABSTRACT: The classical 3D discrete frustrated 4 (DIFFOUR) model is studied with Monte Carlo techniques. The phase diagram is topologically identical with that calculated in mean-field approximation, but the transition temperatures are different. This allows a comparison with experimental phase diagrams.
  EPL (Europhysics Letters) 01/2007; 53(2):216. · 2.17 Impact Factor
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  Available from: Andrey E. Antipov

  Article: Optical echo in photonic crystals

  A. E. Antipov, A. N. Rubtsov
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  ABSTRACT: The dynamics of photonic wavepacket in the effective oscillator potential is studied. The oscillator potential is constructed on a base of one dimensional photonic crystal with a period of unit cell adiabatically varied in space. The structure has a locally equidistant discrete spectrum. This leads to an echo effect, i.e. the periodical reconstruction of the packet shape. The effect can be observed in a nonlinear response of the system. Numerical estimations for porous-silicon based structures are presented for femtosecond Ti:Sapphire laser pump. Comment: 4 pages
  12/2006;
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  Available from: arxiv.org

  Article: Analytic Continuation of Quantum Monte Carlo Data: Optimal Stochastic Regularization Approach

  I. S. Krivenko, A. N. Rubtsov
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  ABSTRACT: A new algorithm for analytic continuation of noisy quantum Monte Carlo (QMC) data from the Matsubara domain to real frequencies is proposed. Unlike the widely used maximum-entropy (MaxEnt) procedure, our method is linear with respect to input data and can therefore be applied to off-diagonal components of a thermal Green's function, or to a self-energy function. The latter possibility is used to analyze QMC results for the half-filled single-band Hubbard model on a Bethe lattice at a low temperature. Our method qualitatively resolves peaks near the inner edges of the Hubbard bands in the vicinity of a Mott transition, whereas a MaxEnt procedure does not. An existence of such structures has been clearly established before in a high-precision D-DMRG calculation by Karski et al. We also analyze a stability of the new method subject to changes of adjustable parameters.
  12/2006;