R. Bulla

University of Cologne, Köln, North Rhine-Westphalia, Germany

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Publications (74)240.35 Total impact

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    ABSTRACT: We revisit the physics of a Kondo impurity coupled to a fermionic host with a diverging power-law density of states near the Fermi level, $\rho(\omega) \sim |\omega|^r$, with exponent -1<r<0. Using the analytical understanding of several fixed points, based partially on powerful mappings between models with bath exponents r and (-r), combined with accurate numerical renormalization group calculations, we determine thermodynamic quantities within the stable phases, and also near the various quantum phase transitions. Antiferromagnetic Kondo coupling leads to strong screening with a negative zero-temperature impurity entropy, while ferromagnetic Kondo coupling can induce a stable fractional spin moment. We formulate the quantum field theories for all critical fixed points of the problem, which are fermionic in nature and allow for a perturbative renormalization-group treatment.
    Physical Review B 08/2013; 88(19). · 3.66 Impact Factor
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    ABSTRACT: The Numerical Renormalization Group is used to solve quantum impurity problems, which describe magnetic impurities in metals, nanodevices, and correlated materials within DMFT. Here we present a conceptually and technically simple generalization of the Wilson Chain, avoiding the exponential scaling of complexity with the number of channels/bands. The method is applied to calculate the t-matrix of the three-channel Kondo model at T=0, which shows universal crossovers in the vicinity of non-Fermi liquid critical points. A non-integrable three-impurity problem with three bands is also studied, revealing a rich phase diagram and novel screening/overscreening mechanisms.
    08/2013; 89(12).
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    ABSTRACT: In recent years the numerical renormalization group (NRG) method has been extended to the calculation of dynamic response functions and transport properties of magnetic impurity models. The approach can now be applied more widely to lattice models of strongly correlated electron systems by the use of dynamical mean field theory (DMFT), in which the lattice problem is transformed into one for an effective impurity with an additional self-consistency constraint. We review these developments and assess the potential for further applications of this approach. We also discuss an alternative approach to renormalization, renormalized perturbation theory, in which the leading asymptotically exact results for the low temperature regime for a number of magnetic impurity models can be obtained within finite order perturbation theory.
    International Journal of Modern Physics B 01/2012; 15(19n20). · 0.46 Impact Factor
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    ABSTRACT: The existence of a length-scale $\xi_K\sim 1/T_K$ (with $T_K$ the Kondo temperature) has long been predicted in quantum impurity systems. At low temperatures $T\ll T_K$, the standard interpretation is that a spin-$\tfrac{1}{2}$ impurity is screened by a surrounding `Kondo cloud' of spatial extent $\xi_K$. We argue that renormalization group (RG) flow between any two fixed points (FPs) results in a characteristic length-scale, observed in real-space as a crossover between physical behaviour typical of each FP. In the simplest example of the Anderson impurity model, three FPs arise; and we show that `free orbital', `local moment' and `strong coupling' regions of space can be identified at zero temperature. These regions are separated by two crossover length-scales $\xi_{\text{LM}}$ and $\xi_K$, with the latter diverging as the Kondo effect is destroyed on increasing temperature through $T_K$. One implication is that moment formation occurs inside the `Kondo cloud', while the screening process itself occurs on flowing to the strong coupling FP at distances $\sim \xi_K$. Generic aspects of the real-space physics are exemplified by the two-channel Kondo model, where $\xi_K$ now separates `local moment' and `overscreening' clouds.
    Physical review. B, Condensed matter 05/2011; 84. · 3.77 Impact Factor
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    ABSTRACT: The bosonic single-impurity Anderson model (B-SIAM) is studied to understand the local dynamics of an atomic quantum dot (AQD) coupled to a Bose-Einstein condensation (BEC) state, which can be implemented to probe the entanglement and the decoherence of a macroscopic condensate. Our recent approach of the numerical renormalization-group calculation for the B-SIAM revealed a zero-temperature phase diagram, where a Mott phase with local depletion of normal particles is separated from a BEC phase with enhanced density of the condensate. As an extension of the previous work, we present the calculations of the local dynamical quantities of the B-SIAM which reinforce our understanding of the physics in the Mott and the BEC phases.
    Physical review. B, Condensed matter 08/2010; 82(5). · 3.77 Impact Factor
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    M. Vojta, L. Fritz, R. Bulla
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    ABSTRACT: Magnetic impurities in neutral graphene provide a realization of the pseudogap Kondo model, which displays a quantum phase transition between phases with screened and unscreened impurity moment. Here, we present a detailed study of the pseudogap Kondo model with finite chemical potential μ. While carrier doping restores conventional Kondo screening at lowest energies, properties of the quantum critical fixed point turn out to influence the behavior over a large parameter range. Most importantly, the Kondo temperature TK shows an extreme asymmetry between electron and hole doping. At criticality, depending on the sign of μ, TK follows either the scaling prediction TK∝|μ| with a universal prefactor, or TK∝|μ|x with x≈2.6. This asymmetry between electron and hole doping extends well outside the quantum critical regime and also implies a qualitative difference in the shape of the tunneling spectra for both signs of μ.
    EPL (Europhysics Letters) 05/2010; 90(2):27006. · 2.26 Impact Factor
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    ABSTRACT: The bosonic single-impurity Anderson model (B-SIAM) is studied to understand the local dynamics of an atomic quantum dot (AQD) coupled to a Bose-Einstein condensation (BEC) state, which can be implemented to probe the entanglement and the decoherence of a macroscopic condensate. Our recent approach of the numerical renormalization group (NRG) calculation for the B-SIAM revealed a zero-temperature phase diagram, where a Mott phase with local depletion of normal particles is separated from a BEC phase with enhanced density of the condensate. As an extension of the previous work, we present the calculations of the local dynamical quantities of the B-SIAM which reinforce our understanding of the physics in the Mott and the BEC phases.
    04/2010;
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    ABSTRACT: We investigate the charge transfer characteristics of one and two excess charges in a DNA base-pair dimer using a model Hamiltonian approach. The electron part comprises diagonal and off-diagonal Coulomb matrix elements such a correlated hopping and the bond-bond interaction, which were recently calculated by Starikov [E. B. Starikov, Phil. Mag. Lett. {\bf 83}, 699 (2003)] for different DNA dimers. The electronic degrees of freedom are coupled to an ohmic or a super-ohmic bath serving as dissipative environment. We employ the numerical renormalization group method in the nuclear tunneling regime and compare the results to Marcus theory for the thermal activation regime. For realistic parameters, the rate that at least one charge is transferred from the donor to the acceptor in the subspace of two excess electrons significantly exceeds the rate in the single charge sector. Moreover, the dynamics is strongly influenced by the Coulomb matrix elements. We find sequential and pair transfer as well as a regime where both charges remain self-trapped. The transfer rate reaches its maximum when the difference of the on-site and inter-site Coulomb matrix element is equal to the reorganization energy which is the case in a GC-GC dimer. Charge transfer is completely suppressed for two excess electrons in AT-AT in an ohmic bath and replaced by damped coherent electron-pair oscillations in a super-ohmic bath. A finite bond-bond interaction $W$ alters the transfer rate: it increases as function of $W$ when the effective Coulomb repulsion exceeds the reorganization energy (inverted regime) and decreases for smaller Coulomb repulsion.
    Physical review. B, Condensed matter 11/2009; 82:195106. · 3.77 Impact Factor
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    ABSTRACT: We discuss a particular source of error in the Numerical Renormalization Group (NRG) method for quantum impurity problems, which is related to a renormalization of impurity parameters due to the bath propagator. At any step of the NRG calculation, this renormalization is only partially taken into account, leading to systematic variation of the impurity parameters along the flow. This effect can cause qualitatively incorrect results when studying quantum critical phenomena, as it leads to an implicit variation of the phase transition's control parameter as function of the temperature and thus to an unphysical temperature dependence of the order-parameter mass. We demonstrate the mass-flow effect for bosonic impurity models with a power law bath spectrum, J(w) ~ w^s, namely the dissipative harmonic oscillator and the spin-boson model. We propose an extension of the NRG to correct the mass-flow error. Using this, we find unambiguous signatures of a Gaussian critical fixed point in the spin-boson model for s<1/2, consistent with mean-field behavior as expected from quantum-to-classical mapping. Comment: 13 pages, 11 figs
    Physical review. B, Condensed matter 11/2009; · 3.77 Impact Factor
  • Physical Review Letters 06/2009; 102(24). · 7.73 Impact Factor
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    ABSTRACT: A continuous time cluster algorithm for two-level systems coupled to a dissipative bosonic bath is presented and applied to the sub-Ohmic spin-boson model. When the power s of the spectral function Jomega proportional, variant omegas is smaller than 1/2, the critical exponents are found to be classical, mean-field like. Potential sources for the discrepancy with recent renormalization group predictions are traced back to the effect of a dangerously irrelevant variable.
    Physical Review Letters 02/2009; 102(3):030601. · 7.73 Impact Factor
  • R. Bulla
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    ABSTRACT: . When a system of correlated electrons is embedded in a dissipative environment, new emergent phenomena might occur due to the interplay of correlation and dissipation. Here we focus on quantum impurity systems with coupling to a bosonic bath. For the theoretical investigation we introduce the bosonic numerical renormalization group method which has been initially set up for the spin-boson model. The role of both correlations and dissipation is described in the context of two-electron transfer systems. We also discuss prospects for the investigation of lattice models of correlated electrons with coupling to a dissipative bath.
    The European Physical Journal Special Topics 01/2009; · 1.80 Impact Factor
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    ABSTRACT: We investigate nonequilibrium two-electron transfer in a model redox system represented by a two-site extended Hubbard model and embedded in a dissipative environment. The influence of the electron-electron interactions and the coupling to a dissipative bosonic bath on the electron transfer is studied in different temperature regimes. At high temperatures, Marcus transfer rates are evaluated, and at low temperatures, we calculate equilibrium and nonequilibrium population probabilities of the donor and acceptor with the nonperturbative numerical renormalization group approach. We obtain the nonequilibrium dynamics of the system prepared in an initial state of two electrons at the donor site and identify conditions under which the electron transfer involves one concerted two-electron step or two sequential single-electron steps. The rates of the sequential transfer depend nonmonotonically on the difference between the intersite and on-site Coulomb interaction, which become renormalized in the presence of the bosonic bath. If this difference is much larger than the hopping matrix element, the temperature as well as the reorganization energy, simultaneous transfer of both electrons between donor and acceptor can be observed.
    Physical review. B, Condensed matter 07/2008; 78(3). · 3.77 Impact Factor
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    ABSTRACT: We use the numerical renormalization group method (NRG) to investigate a single-impurity Anderson model with a coupling of the impurity to a superconducting host. Analysis of the energy flow shows that, contrary to previous belief, NRG iterations can be performed up to a large number of sites, corresponding to energy differences far below the superconducting gap Δ. This allows us to calculate the impurity spectral function A(ω) very accurately for frequencies |ω|∼Δ, and to resolve, in a certain parameter regime, sharp peaks in A(ω) close to the gap edge.
    Journal of Physics Condensed Matter 07/2008; 20(27):275213. · 2.22 Impact Factor
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    ABSTRACT: We investigate non-equilibrium two-electron transfer in a model redox system represented by a two-site extended Hubbard model and embedded in a dissipative environment. The influence of the electron-electron interactions and the coupling to a dissipative bosonic bath on the electron transfer is studied in different temperature regimes. At high temperatures Marcus transfer rates are evaluated and at low temperatures, we calculate equilibrium and non-equilibrium population probabilities of the donor and acceptor with the non-perturbative Numerical Renormalization Group approach. We obtain the non-equilibrium dynamics of the system prepared in an initial state of two electrons at the donor site and identify conditions under which the electron transfer involves one concerted two-electron step or two sequential single-electron steps. The rates of the sequential transfer depend non-monotonically on the difference between the inter-site and on-site Coulomb interaction which become renormalized in the presence of the bosonic bath. If this difference is much larger than the hopping matrix element, the temperature as well as the reorganization energy, simultaneous transfer of both electrons between donor and acceptor can be observed.
    04/2008;
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    ABSTRACT: Electron transfer processes play a central role in many chemical and biological systems. Already the transfer of a single electron from the donor to the acceptor can be viewed as a complicated many-body problem, due to the coupling of the electron to the infinitely many environmental degrees of freedom, realized by density fluctuations of the solvent or molecular vibrations of the protein matrix. We focus on the quantum mechanical modelling of two-electron transfer processes whose dynamics is governed by the Coulomb interaction between the electrons as well as the environmental degrees of freedoms represented by a bosonic bath. We identify the regime of parameters in which concerted transfer of the two electrons occurs and discuss the influence of the Coulomb repulsion and the coupling strength to the environment on the electron transfer rate. Calculations are performed using the non-perturbative numerical renormalization group approach for both equilibrium and non-equilibrium properties.
    01/2008: pages 69-78;
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    ABSTRACT: We address the quantum transition of a spin-1/2 antiferromagnetic Kondo lattice model with an easy-axis anisotropy using the extended dynamical mean field theory. We derive results in real frequency by using the bosonic numerical renormalization group (BNRG) method and compare them with quantum Monte Carlo results in Matsubara frequency. The BNRG results show a logarithmic divergence in the critical local spin susceptibility, signaling a destruction of Kondo screening. The T=0 transition is consistent with being second order. The BNRG results also display some subtle features; we identify their origin and suggest means for further microscopic studies.
    Physical Review Letters 12/2007; 99(22):227204. · 7.73 Impact Factor
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    ABSTRACT: We systematically study the influence of ferromagnetic leads on the Kondo resonance in a quantum dot tuned to the local moment regime. We employ Wilson's numerical renormalization group method, extended to handle leads with a spin asymmetric density of states, to identify the effects of (i) a finite spin polarization in the leads (at the Fermi-surface), (ii) a Stoner splitting in the bands (governed by the band edges) and (iii) an arbitrary shape of the leads density of states. For a generic lead density of states the quantum dot favors being occupied by a particular spin-species due to exchange interaction with ferromagnetic leads leading to a suppression and splitting of the Kondo resonance. The application of a magnetic field can compensate this asymmetry restoring the Kondo effect. We study both the gate-voltage dependence (for a fixed band structure in the leads) and the spin polarization dependence (for fixed gate voltage) of this compensation field for various types of bands. Interestingly, we find that the full recovery of the Kondo resonance of a quantum dot in presence of leads with an energy dependent density of states is not only possible by an appropriately tuned external magnetic field but also via an appropriately tuned gate voltage. For flat bands simple formulas for the splitting of the local level as a function of the spin polarization and gate voltage are given.
    Physical review. B, Condensed matter 06/2007; 76(4). · 3.77 Impact Factor
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    ABSTRACT: Employing the nonperturbative numerical renormalization group method, we study the dynamics of the spin-boson model, which describes a two-level system coupled to a bosonic bath with a spectral density J(omega) proportional to omega(s). We show that, in contrast with the case of Ohmic damping, the delocalized phase of the sub-Ohmic model cannot be characterized by a single energy scale only, due to the presence of a nontrivial quantum phase transition. In the strongly sub-Ohmic regime, s<1, weakly damped coherent oscillations on short time scales are possible even in the localized phase--this is of crucial relevance, e.g., for qubits subject to electromagnetic noise.
    Physical Review Letters 05/2007; 98(21):210402. · 7.73 Impact Factor
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    ABSTRACT: In the beginning of the 1970's, Wilson developed the concept of a fully non-perturbative renormalization group transformation. Applied to the Kondo problem, this numerical renormalization group method (NRG) gave for the first time the full crossover from the high-temperature phase of a free spin to the low-temperature phase of a completely screened spin. The NRG has been later generalized to a variety of quantum impurity problems. The purpose of this review is to give a brief introduction to the NRG method including some guidelines of how to calculate physical quantities, and to survey the development of the NRG method and its various applications over the last 30 years. These applications include variants of the original Kondo problem such as the non-Fermi liquid behavior in the two-channel Kondo model, dissipative quantum systems such as the spin-boson model, and lattice systems in the framework of the dynamical mean field theory.
    Review of Modern Physics 02/2007; · 44.98 Impact Factor

Publication Stats

2k Citations
240.35 Total Impact Points

Institutions

  • 2009–2013
    • University of Cologne
      • Institute for Theoretical Physics
      Köln, North Rhine-Westphalia, Germany
    • Universität des Saarlandes
      • Physikalische und Theoretische Chemie
      Saarbrücken, Saarland, Germany
  • 1999–2012
    • Universität Augsburg
      • Institute of Physics
      Augsberg, Bavaria, Germany
    • Max Planck Institute of Physics
      München, Bavaria, Germany
  • 2008
    • Ludwig-Maximilian-University of Munich
      • Department of Physics
      München, Bavaria, Germany
  • 2007
    • Universität Bremen
      Bremen, Bremen, Germany
  • 2006
    • Renmin University of China
      • Department of Physics
      Peping, Beijing, China
  • 2005
    • Karlsruhe Institute of Technology
      • Institute of Theoretical Condensed Matter Physics
      Karlsruhe, Baden-Wuerttemberg, Germany
  • 1997–2002
    • Imperial College London
      • Department of Mathematics
      London, ENG, United Kingdom
  • 1994–1995
    • Universität Regensburg
      • Intitute of Theoretical Physics
      Ratisbon, Bavaria, Germany