Iterative Perturbation Theory Research Articles

Random Local Attraction Driven Metal–Superconductor Transition

In this paper, we investigate the disordered attractive Hubbard model by combining dynamical mean field theory, coherent potential approximation and iterated perturbation theory for superconductivity as an impurity solver. Disorder is introduced in the local attraction $U$. We assume that $U$ is distributed according to a bimodal probability distribution, wherein an $x$ fraction of sites are pairing centers ($U\neq0$) and $(1-x)$ fraction of sites are non-interacting ($U=0$). It is found that beyond a critical $x=x_c$, a first order metal-superconductor phase transition leads to superconductivity being induced in the interacting as well as non-interacting.

Alternative Equation of Motion Approach to the Single-Impurity Anderson Model

Solving the single-impurity Anderson model is a basic problem of solid state physics. The single-impurity Anderson model is very important, at present it is also used for systems with quantum impurities, e.g. semiconductor quantum dots and molecular transistors. Its main application is in the scheme of dynamical mean eld theory describing strong correlation electron systems. To solve the single-impurity Anderson model problem we use the equation of motion Green function approach. In this report we present the novel equation of motion approximation in which we di erentiate the Green function over both time variables. This di ers from the commonly used equation of motion solution by Appelbaum, Penn and Lacroix where the authors take time derivative only over primary time variable. After extending calculations to higher order Green functions we nd the new approximate dynamical solution of single-impurity Anderson model. The results are compared with the solutions to the single-impurity Anderson model problem at intermediate Coulomb repulsion U such as the modi ed iterative perturbation theory. Our approach is suitable for describing quantum dots.

Non-equilibrium STLS approach to transport properties of single impurity Anderson model

In this work, using the non-equilibrium Keldysh formalism, we study the effects of the electron–electron interaction and the electron-spin correlation on the non-equilibrium Kondo effect and the transport properties of the symmetric single impurity Anderson model (SIAM) at zero temperature by generalizing the self-consistent method of Singwi, Tosi, Land, and Sjolander (STLS) for a single-band tight-binding model with Hubbard type interaction to out of equilibrium steady-states. We at first determine in a self-consistent manner the non-equilibrium spin correlation function, the effective Hubbard interaction, and the double-occupancy at the impurity site. Then, using the non-equilibrium STLS spin polarization function in the non-equilibrium formalism of the iterative perturbation theory (IPT) of Yosida and Yamada, and Horvatic and Zlatic, we compute the spectral density, the current–voltage characteristics and the differential conductance as functions of the applied bias and the strength of on-site Hubbard interaction. We compare our spectral densities at zero bias with the results of numerical renormalization group (NRG) and depict the effects of the electron–electron interaction and electron-spin correlation at the impurity site on the aforementioned properties by comparing our numerical result with the order U2 IPT. Finally, we show that the obtained numerical results on the differential conductance have a quadratic universal scaling behavior and the resulting Kondo temperature shows an exponential behavior.

Multiorbital effects on thermoelectric properties of strongly correlated materials

The effects of electronic correlations and orbital degeneracy on thermoelectric properties are studied within the context of multi-orbital Hubbard models on different lattices. We use dynamical mean field theory with iterative perturbation theory as a solver to calculate the self-energy of the models in wide range of interaction strengths. The Seebeck coefficient, which measures the voltage drop in response to a temperature gradient across the system, shows a non-monotonic behavior with temperatures in the presence of strong correlations. This anomalous behavior is associated with a crossover from a Fermi liquid metal at low temperatures to a bad metal with incoherent excitations at high temperatures. We find that for interactions comparable to the bandwidth the Seebeck coefficient acquires large values at low temperatures. Moreover, for strongly correlated cases, where the interaction is larger than the band width, the figure of merit is enhanced over a wide range of temperatures because of decreasing electronic contributions to the thermal conductivity. We also find that multi-orbital systems will typically yield larger thermopower compared to single orbital models.

Coulomb Scattering in the Massless Nelson Model I. Foundations of Two-Electron Scattering

We construct two-electron scattering states and verify their tensor product structure in the infrared-regular massless Nelson model. The proof follows the lines of Haag-Ruelle scattering theory: Scattering state approximants are defined with the help of two time-dependent renormalized creation operators of the electrons acting on the vacuum. They depend on ground state wave functions of the (single-electron) fiber Hamiltonians with infrared cut-off. Convergence of these approximants as $t\to \infty$ is shown with the help of Cook's method combined with a non-stationary phase argument. Removal of the infrared cut-off in the limit $t\to \infty$ requires sharp estimates on the derivatives of these ground state wave functions w.r.t. electron and photon momenta, with mild dependence on the infrared cut-off. These key estimates, which carry information about the localization of electrons in space, are obtained in a companion paper with the help of iterative analytic perturbation theory. Our results hold in the weak coupling regime.

Equation of motion solutions to Hubbard model retaining Kondo effect

We propose a new way of analyzing the Hubbard model using equations of motion (EOM) for the higher-order Green's functions approach within the DMFT scheme. In calculating the higher order Green function we will differentiate over both times (t) and (t′). This allows us to obtain the metallic Fermi liquid at nonzero Coulomb interaction, where the three center DOS structure with two Hubbard bands and the quasiparticle resonance peak is obtained. At small Coulomb interactions and zero temperature the height of the quasiparticle resonance peak on the Fermi energy is constant similarly as in the full DMFT method with numerical (Quantum Monte Carlo) or with analytical (e.g. iterative perturbation theory) calculations.

The Mass Shell in the Semi-Relativistic Pauli–Fierz Model

We consider the semi-relativistic Pauli-Fierz model for a single free electron interacting with the quantized radiation field. Employing a variant of Pizzo's iterative analytic perturbation theory we construct a sequence of ground state eigenprojections of infra-red cutoff, dressing transformed fiber Hamiltonians and prove its convergence, as the cutoff goes to zero. Its limit is the ground state eigenprojection of a certain Hamiltonian unitarily equivalent to a renormalized fiber Hamiltonian acting in a coherent state representation space. The ground state energy is an exactly two-fold degenerate eigenvalue of the renormalized Hamiltonian, while it is not an eigenvalue of the original fiber Hamiltonian unless the total momentum is zero. These results hold true, for total momenta inside a ball about zero of arbitrary radius p>0, provided that the coupling constant is sufficiently small depending on p and the ultra-violet cutoff. Along the way we prove twice continuous differentiability and strict convexity of the ground state energy as a function of the total momentum inside that ball.

Benchmark of a modified iterated perturbation theory approach on the fcc lattice at strong coupling

The Dynamical Mean-Field theory (DMFT) approach to the Hubbard model requires a method to solve the problem of a quantum impurity in a bath of non-interacting electrons. Iterated Perturbation Theory (IPT) has proven its effectiveness as a solver in many cases of interest. Based on general principles and on comparisons with an essentially exact Continuous-Time Quantum Monte Carlo (CTQMC) solver, here we show that the standard implementation of IPT fails away from half-filling when the interaction strength is much larger than the bandwidth. We propose a slight modification to the IPT algorithm that replaces one of the equations by the requirement that double occupancy calculated with IPT gives the correct value. We call this method IPT-$D$. We recover the Fermi liquid ground state away from half-filling. The Fermi liquid parameters, density of states, chemical potential, energy and specific heat on the FCC lattice are calculated with both IPT-$D$ and CTQMC as benchmark examples. We also calculated the resistivity and the optical conductivity within IPT-$D$. Particle-hole asymmetry persists even at coupling twice the bandwidth. Several algorithms that speed up the calculations are described in appendices.

Correlation effects in two-dimensional topological insulators

We investigate correlation effects in two-dimensional topological insulators (TI). In the first part, we discuss finite size effects for interacting systems of different sizes in a ribbon geometry. For large systems, there are two pairs of well separated massless modes on both edges. For these systems, we analyze the finite size effects using a standard bosonization approach. For small systems, where the edge states are massive Dirac fermions, we use the inhomogeneous dynamical mean-field theory (DMFT) combined with iterative perturbation theory as an impurity solver to study interaction effects. We show that the finite size gap in the edge states is renormalized for weak interactions, which is consistent with a Fermi-liquid picture for small size TIs. In the second part, we investigate phase transitions in finite size TIs at zero temperature focusing on the effects of possible interedge umklapp scattering for the edge states within the inhomogeneous DMFT using the numerical renormalization group. We show that correlation effects are effectively stronger near the edge sites because the coordination number is smaller than in the bulk. Therefore the localization of the edge states around the edge sites, which is a fundamental property in TIs, is weakened for strong coupling strengths. However, we find no signs for ``edge Mott insulating states'' and the system stays in the topological insulating state, which is adiabatically connected to the noninteracting state for all interaction strengths smaller than the critical value. Increasing the interaction further, a nearly homogeneous Mott insulating state is stabilized.

Description of Quasi Particle Bands of Ce Compounds Using the Wannier Representation

We present a method to describe the quasi-particle bands of heavy-fermion Ce compounds on the basis of the periodic Anderson model taking account of the realistic conduction-band structures using the Wannier functions. We first calculate the conduction-band structure of the corresponding La compound by the pseudo potential method, and represent it by the maximally localized Wannier functions, and then consider the hybridizations between these conduction bands and the 4 f -electron eigen states of the spin–orbit coupling and crystalline electric field by the use of the Slater–Koster integrals. To take into account the correlation effects of the 4 f electrons, we adopt the dynamical mean field theory with the iterative perturbation theory as an impurity solver to obtain the quasi particle bands. We apply this method to describe the quasi particle bands of CeRu 2 Si 2 exhibiting the paramagnetic heavy-fermion states at extremely low temperatures.

TRANSPORT AND SPECTRA IN THE HALF-FILLED HUBBARD MODEL: A DYNAMICAL MEAN FIELD STUDY

We present an improved numerical implementation of the iterated perturbation theory, for use as an impurity solver for lattice models within dynamical mean field theory (DMFT). We demonstrate higher resolution of spectral and transport features and a reduced computational expense. Using this implementation, we study the issues of scaling and universality in spectral and transport properties of the particle-hole symmetric Hubbard model within DMFT. We re-examine experimental results for pressure-dependent resistivity in Selenium doped NiS2and thermal hysteresis on V2O3and find qualitative agreement. A systematic study of spectral weight transfer in optical conductivity is carried out.

Nonequilibrium transport theory of the singlet-triplet transition: Perturbative approach

We use a simple iterative perturbation theory to study the singlet-triplet (ST) transition in lateral and vertical quantum dots, modeled by the nonequilibrium two-level Anderson model. To a great surprise, the region of stable perturbation theory extends to relatively strong interactions, and this simple approach is able to reproduce all experimentally observed features of the ST transition, including the formation of a dip in the differential conductance of a lateral dot indicative of the two-stage Kondo effect, or the maximum in the linear conductance around the transition point. Choosing the right starting point to the perturbation theory is, however, crucial to obtain reliable and meaningful results.

Interaction quench in the Hubbard model: Relaxation of the spectral function and the optical conductivity

We use nonequilibrium dynamical mean-field theory in combination with a recently developed Quantum Monte Carlo impurity solver to study the real-time dynamics of a Hubbard model which is driven out of equilibrium by a sudden increase in the on-site repulsion $U$. We discuss the implementation of the self-consistency procedure and some important technical improvements of the QMC method. The exact numerical solution is compared to iterated perturbation theory, which is found to produce accurate results only for weak interaction or short times. Furthermore, we calculate the spectral functions and the optical conductivity from a Fourier transform on the finite Keldysh contour, for which the numerically accessible time scales allow to resolve the formation of Hubbard bands and a gap in the strongly interacting regime. The spectral function, and all one-particle quantities that can be calculated from it, thermalize rapidly at the transition between qualitatively different weak- and strong-coupling relaxation regimes.

Dynamical Mean Field Theory for d Electrons on Cubic Lattices with Realistic Electron Hopping and Interaction

The noncrossing approximation (NCA) for solving an impurity problem of interacting electrons is applied to the dynamical mean field theory for a d -electron system on cubic lattices. Anisotropy in the hopping integrals as well as intraatomic Coulomb interactions and the crystalline field splitting of d orbitals are fully considered. Single-particle excitation spectra are calculated for various occupations of the d band and discussed with reference to the multiplet spectra obtained in the NCA calculation and the k -dependent spectra. Differences in the results of the NCA and the iterative perturbation theory are discussed.

Dynamical mean field theory equations on nearly real frequency axis

The iterated perturbation theory (IPT) equations of the dynamical mean field theory (DMFT) for the half-filled Hubbard model are solved on nearly real frequencies at various values of the Hubbard parameters, U, to investigate the nature of metal–insulator transition (MIT) at finite temperatures. This method avoids the instabilities associated with the infamous Padé analytic continuation and reveals fine structures across the MIT at finite temperatures, which cannot be captured by conventional methods for solving DMFT-IPT equations on Matsubara frequencies. Our method suggests that at finite temperatures, there is a crossover from a bad metal to a bad insulator in which the height of the quasi-particle (Kondo) peak decreases to a non-zero small bump, which gradually suppresses as one moves deeper into the bad insulating regime.

Renormalized Electron Mass in Nonrelativistic QED

Within the framework of nonrelativistic QED, we prove that, for small values of the coupling constant, the energy function, E_|P|, of a dressed electron is twice differentiable in the momentum P in a neighborhood of P = 0. Furthermore, (E_|P|)" is bounded from below by a constant larger than zero. Our results are proven with the help of iterative analytic perturbation theory.

Correlation effect on the Van Vleck susceptibility in Sr2RuO4

We have studied the effect of electron correlation on Pauli (χP) and Van Vleck (χVV) susceptibility in Sr2RuO4 by adopting the dynamical mean-field theory with the iterative perturbation theory as an impurity solver. For non-interacting case, χVV/χP≃0.5 is obtained near the superconducting transition temperature, while in the presence of electron correlation, χVV/χP tends to become smaller than 0.5, due to the stronger renormalization effect of χP, compared with χVV. On the basis of this result, we have discussed the Knight shift experiment of this material.

Perturbation study of nonequilibrium quasiparticle spectra in an infinite-dimensional Hubbard lattice

A model for nonequilibrium dynamical mean-field theory is constructed for the infinite-dimensional Hubbard lattice. We impose nonequilibrium by expressing the physical orbital as a superposition of a left $(L)$-moving and right $(R)$-moving electronic state with the respective chemical potentials ${\ensuremath{\mu}}_{L}$ and ${\ensuremath{\mu}}_{R}$. Using the second-order iterative perturbation theory we calculate the quasiparticle properties as a function of the chemical potential bias between the $L$ and $R$ movers, i.e., $\ensuremath{\Phi}={\ensuremath{\mu}}_{L}\ensuremath{-}{\ensuremath{\mu}}_{R}$. The evolution of the nonequilibrium quasiparticle spectrum is mapped out as a function of the bias and temperature. The quasiparticle states with the renormalized Fermi-energy scale ${\ensuremath{\epsilon}}_{QP}^{0}$ disappear at $\ensuremath{\Phi}\ensuremath{\sim}{\ensuremath{\epsilon}}_{QP}^{0}$ in the low-temperature limit. The second-order perturbation theory predicts that in the vicinity of the Mott-insulator transition at the Coulomb-parameter $U={U}_{c}$, there exists another critical Coulomb-parameter ${U}_{d}$ $(l{U}_{c})$ such that, for ${U}_{d}lUl{U}_{c}$, quasiparticle states are destroyed abruptly when ${({\ensuremath{\epsilon}}_{QP}^{0})}^{2}\ensuremath{\sim}a{(\ensuremath{\pi}{k}_{B}{T}_{c})}^{2}+b{\ensuremath{\Phi}}_{c}^{2}$ with the critical temperature ${T}_{c}$, the critical bias ${\ensuremath{\Phi}}_{c}$, and the numerical constants $a$ and $b$ on the order of unity.

Theory of Two-Photon Absorption Spectrum in Mott Insulators Based on Dynamical Cluster Approximation

We investigate the two-photon absorption (TPA) spectrum in Mott insulators on the basis of dynamical cluster approximation. The nonlocal correlation is found to be important in enhancing the dimensionality dependence of the TPA spectrum. The dependence of the TPA spectrum on Coulomb interaction is modified compared with that of the dynamical mean field theory, which is also caused by a nonlocal correlation through a one-particle spectrum. We compare several degrees of nonlocality by adjusting the cluster momentum. The iterated perturbation theory is adopted as an impurity solver, and then a comparison with the noncrossing approximation is presented. It is confirmed that the predominant optical process in Mott insulators is different from that of conventional semiconductors, and small Mott insulating gaps are favorable for obtaining a large TPA spectrum.

Generalization of iterative perturbation theory and coherent potential approximation (ITP+CPA) to double exchange model with orbital degeneracy

A combination of the iterative perturbation theory (ITP) of the dynamical mean field theory (DMFT) and coherent-potential approximation (CPA) is generalized to the double exchange model with orbital degeneracy. The Hubbard interaction and the off-diagonal components for the hopping matrix tmnij(m ≠ n) are considered in our calculation of spectrum and optical conductivity. The numerical results show that the effects of the non-diagonal hopping matrix elements are important.