Self-consistent Perturbation Theory Research Articles

Origin of anomalous specific heat coefficient of YbAl3

By using recently proposed effective model for heavy fermion metallic systems, the temperature dependence of the specific heat coefficient of typical heavy fermion material YbAl3 is investigated. The Hamiltonian of the band term consists of the conduction electrons described with nearly free electron method, the localized 4f electrons of Yb ions and the hybridization term between the conduction and 4f electrons. In order to take account of the correlation effect, we reconstruct the low-energy effective Hamiltonian where the low-energy bands near the Fermi level are extracted. The self-consistent perturbation theory with local approximation is applied to this Hamiltonian, so that some physical quantities are calculated. The obtained temperature dependence of the specific heat divided by temperature shows two peak structures, which are in agreement with the experimental results of YbAl3. We show that one peak structure at the very low temperature region originates from the correlation effect and the other peak structure results from the band structure.

Modeling superconducting states of arbitrary pairing symmetry with the fluctuation exchange approximation applied to Hubbard-like models

We present an algorithm for microscopic modeling of superconducting states of arbitrary pairing symmetry via an implementation of self-consistent perturbation theory, the fluctuation exchange approximation (FLEX), applied to Hubbard-like models. Like the original formulation of FLEX, all ring diagrams that are generated with the bare interaction vertex are included in the generating functional for the self-energy. Thus, this algorithm is suitable for FLEX-based Hubbard model calculations in both the attractive and repulsive cases.

Specific Heat-Coefficient of YbAl3 Studied by Combined Nearly Free Electron Conduction Band Hybridized with Localized f Electrons with Correlation Effect

Based on the recently proposed band model, the electronic specific heat of moderately heavy electron compound YbAl$_3$ are investigated. The band term of the Hamiltonian consists of three parts; conduction electrons described by the nearly free electron method, localized 4f electrons of Yb ions and the hybridization term between these electrons. Extracting several bands near the Fermi level, we reconstruct the low-energy effective Hamiltonian in order to consider the correlation effect, which is studied by using the self-consistent second order perturbation theory combined with local approximation. The temperature dependence of the specific heat $c_{\rm v}(T)$ is calculated as a function of temperature $T$ from the numerical derivative of the internal energy. Sommerfeld coefficient $\gamma$ is also calculated from the direct formula. The overall structure of $c_{\rm v}(T)/T$ is in quantitative agreement with the experimental results, which have the characteristic two-peak structures. They originate from the correlation effect and the structure of the non-interacting density of states, respectively. We show that our effective Hamiltonian yielding the realistic band structure may describe quantitatively heavy electron compounds with conduction bands composed of s- or p- electrons.

MOLCAS 7: The Next Generation

Some of the new unique features of the MOLCAS quantum chemistry package version 7 are presented in this report. In particular, the Cholesky decomposition method applied to some quantum chemical methods is described. This approach is used both in the context of a straight forward approximation of the two-electron integrals and in the generation of so-called auxiliary basis sets. The article describes how the method is implemented for most known wave functions models: self-consistent field, density functional theory, 2nd order perturbation theory, complete-active space self-consistent field multiconfigurational reference 2nd order perturbation theory, and coupled-cluster methods. The report further elaborates on the implementation of a restricted-active space self-consistent field reference function in conjunction with 2nd order perturbation theory. The average atomic natural orbital basis for relativistic calculations, covering the whole periodic table, are described and associated unique properties are demonstrated. Furthermore, the use of the arbitrary order Douglas-Kroll-Hess transformation for one-component relativistic calculations and its implementation are discussed. This section especially focuses on the implementation of the so-called picture-change-free atomic orbital property integrals. Moreover, the ElectroStatic Potential Fitted scheme, a version of a quantum mechanics/molecular mechanics hybrid method implemented in MOLCAS, is described and discussed. Finally, the report discusses the use of the MOLCAS package for advanced studies of photo chemical phenomena and the usefulness of the algorithms for constrained geometry optimization in MOLCAS in association with such studies.

Correlation effect on effective model with realistic electronic structure for heavy fermion compound YbAl3

Based on the recently proposed effective Hamiltonian for typical heavy fermion compound YbAl3, the correlation effect is systematically investigated in the physical properties. The band part of the Hamiltonian consists of conduction bands described by nearly free electron method, hybridization between the conduction and 4f-electrons, and the localized 4f-states of Yb ions on the lattice site. The correlation effect is considered by using the self-consistent perturbation theory with local approximation. The temperature dependence of the specific heat coefficient is calculated, and the anomalous behaviors are found in the low temperature region in accord with the experiments. We show that the anomalies may originate from the correlation effect and the structure of the non-interacting density of states.

Nonspherical Potential due to Orbital Polarization and Its Effect in Atoms –Approach to Hund's Second Rule in Terms of One-Electron Picture–

The exchange–correlation functional composed of the X α-exchange energy and the new type of correlation energy E M is assumed in order to study the effect of the nonspherical spatial distribution of electrons and the degeneracy of the total energy for states with the different M L values in the electronic open-shell configuration l N ( l = p , d ) of atom, where N is the number of electrons in the open shell characterized by directional quantum number l , M L is an expectation value of the z -component L z of total angular momentum, and E M depends on M L . Nonspherical quantities such as electron density and one-electron effective potential are made from the partially filled occupation obeying Hund's first rule in the open shell, and the Kohn–Sham equation is solved by the self-consistent degenerate first-order perturbation theory. Then, the parameters included in E M are succinctly and conveniently determined by imposing the appropriate conditions of degeneracy on the orbital and total energies. These m...

Self-consistent many-body perturbation theory in range-separated density-functional theory: A one-electron reduced-density-matrix-based formulation

In many cases, density-functional theory (DFT) with current standard approximate functionals offers a relatively accurate and computationally cheap description of the short-range dynamic electron correlation effects. However, in general, standard DFT does not treat the dispersion interaction effects adequately which, on the other hand, can be described by many-body perturbation theory (MBPT). It is therefore of interest to develop a hybrid model which combines the best of both the MBPT and DFT approaches. This can be achieved by splitting the two-electron interaction into long-range and short-range parts; the long-range part is then treated by MBPT and the short-range part by DFT. This work deals with the formulation of a general MBPT-DFT model (i.e., valid for any type of zeroth-order Hamiltonian) based on such a range separation. Applying the Rayleigh-Schr\"odinger formalism in this context, one finds that the generalized Bloch equation becomes self-consistent at each order of perturbation. This complication arises because the short-range part of the energy is a functional of the exact electron density, which is expanded in a perturbation series. In order to address this ``self-consistency problem'' and provide computable orbital-based expressions for any order of perturbation, a general one-electron reduced-density-matrix-based formalism is proposed. Two applications of our general formalism are presented: The derivation of a hybrid second-order M\o{}ller-Plesset-DFT model and the formulation of a range-separated optimized effective potential method based on a hybrid G\"orling-Levy-type MBPT-DFT model.

Anderson impurity model in a semiconductor

We consider an Anderson impurity model in which the locally correlated orbital is coupled to a host with a gapped density of states. Single-particle dynamics are studied within a perturbative framework that includes both explicit second-order perturbation theory and self-consistent perturbation theory to all orders in the interaction. Away from particle-hole symmetry, the system is shown to be a generalized Fermi liquid (GFL) in the sense of being perturbatively connectable to the noninteracting limit, and the exact Friedel sum rule for the GFL phase is obtained. We show by contrast that the particle-hole-symmetric point of the model is not perturbatively connected to the noninteracting limit and as such is a non-Fermi liquid for all nonzero gaps. Our conclusions are in agreement with numerical renormalization group studies of the problem.

Impact of Exchange-Correlation Effects on theIVCharacteristics of a Molecular Junction

The role of exchange-correlation effects in nonequilibrium quantum transport through molecular junctions is assessed by analyzing the IV curve of a generic two-level model using self-consistent many-body perturbation theory (second Born and GW approximations) on the Keldysh contour. It is demonstrated how the variation of the molecule's energy levels with the bias voltage can produce anomalous peaks in the dI/dV curve. This effect is suppressed by electronic self-interactions and is therefore underestimated in standard transport calculations based on density functional theory. Inclusion of dynamic correlations introduces quasiparticle (QP) scattering which in turn broadens the molecular resonances. The broadening increases strongly with bias and can have a large impact on the calculated IV characteristic.

A CASPT2//CASSCF study of the quartet excited state $$\tilde{a}^{4}A^{\prime\prime}$$ of the HCNN radical

Complete active space self-consistent field and second-order multiconfigurational perturbation theory methods have been performed to investigate the quartet excited state \({\tilde{a}}^{4}{A^{\prime\prime}}\) potential energy surface of HCNN radical. Two located minima with respective cis and trans structures could easily dissociate to CH \(({\tilde{a}}^{4}\Sigma^{-})\) and \(N_{2} ({\tilde{X}}^{1}\Sigma_{\rm g}^{+})\) products with similar barrier of about 16.0 kcal/mol. In addition, four minimum energy crossing points on a surface of intersection between \({\tilde{a}}^{4}A^{\prime\prime}\) and X (\(X={\tilde{X}}^{2}A^{\prime\prime}\) and \({\tilde{A}}^{2}A^{\prime}\)) states are located near to the minima. However, the intersystem crossing \({\tilde{a}}^{4}A^{\prime\prime} \rightarrow X\) is weak due to the vanishingly small spin–orbit interactions. It further indicates that the direct dissociation on the \({\tilde{a}}^{4}{A^{\prime\prime}}\) state is more favored. This information combined with the comparison with isoelectronic HCCO provides an indirect support to the recent experimental proposal of photodissociation mechanism of HCNN.

Relativistic calculation of nuclear magnetic shielding tensor using the regular approximation to the normalized elimination of the small component. II. Consideration of perturbations in the metric operator

A previous relativistic shielding calculation theory based on the regular approximation to the normalized elimination of the small component approach is improved by the inclusion of the magnetic interaction term contained in the metric operator. In order to consider effects of the metric perturbation, the self-consistent perturbation theory is used for the case of perturbation-dependent overlap integrals. The calculation results show that the second-order regular approximation results obtained for the isotropic shielding constants of halogen nuclei are well improved by the inclusion of the metric perturbation to reproduce the fully relativistic four-component Dirac-Hartree-Fock results. However, it is shown that the metric perturbation hardly or does not affect the anisotropy of the halogen shielding tensors and the proton magnetic shieldings.

Quasiparticle Self-ConsistentGWTheory

In past decades the scientific community has been looking for a reliable first-principles method to predict the electronic structure of solids with high accuracy. Here we present an approach which we call the quasiparticle self-consistent approximation. It is based on a kind of self-consistent perturbation theory, where the self-consistency is constructed to minimize the perturbation. We apply it to selections from different classes of materials, including alkali metals, semiconductors, wide band gap insulators, transition metals, transition metal oxides, magnetic insulators, and rare earth compounds. Apart from some mild exceptions, the properties are very well described, particularly in weakly correlated cases. Self-consistency dramatically improves agreement with experiment, and is sometimes essential. Discrepancies with experiment are systematic, and can be explained in terms of approximations made.

Kondo transport in a magnetic field through a biased quantum dot

We develop a theory of out-of-equilibrium transport phenomena in a magnetic field based on the self-consistent perturbation theory within the weak correlation regime. Magnetization vanishes in the limit of large bias voltage. The differential conductance splits into double peaks with increasing a magnetic field. The threshold field of the split is reduced when the correlation effect is increased.

Magnetic and transport properties of a quantum dot in nonequilibrium conditions

We discuss structures of the differential conductance in the limit of the large bias voltage and magnetic field by employing the self-consistent perturbation theory up to the fourth order in the Coulomb interaction. It is found that the dips for the strong correlation regime and the peaks for the weak correlation regime, respectively, appear in the differential conductance when the Zeeman energy corresponds to the bias voltage.

Self-Consistent Perturbation Theory for Thermodynamics of Magnetic Impurity Systems

Integral equations for thermodynamic quantities are derived in the framework of the non-crossing approximation (NCA). Entropy and specific heat of 4f contribution are calculated without numerical differentiations of thermodynamic potential. The formulation is applied to systems such as PrFe4P12 with singlet-triplet crystalline electric field (CEF) levels.

X, A, B, C, and D States of the C6H5F+ Ion Studied Using Multiconfiguration Wave Functions

Electronic states of the C6H5F+ ion have been studied within C2v symmetry by using the complete active space self-consistent field (CASSCF) and multiconfiguration second-order perturbation theory (CASPT2) methods in conjunction with an atomic natural orbital basis. Vertical excitation energies (Tv) and relative energies (Tv') at the ground-state geometry of the C6H5F molecule were calculated for 12 states. For the five lowest-lying states, 1(2)B1, 1(2)A2, 2(2)B1, 1(2)B2, and 1(2)A1, geometries and vibrational frequencies were calculated at the CASSCF level, and adiabatic excitation energies (T0) and potential energy curves (PEC) for F-loss dissociations were calculated at the CASPT2//CASSCF level. On the basis of the CASPT2 T0 calculations, we assign the X, A, B, C, and D states of the ion to 1(2)B1, 1(2)A2, 2(2)B1, 1(2)B2, and 1(2)A1, respectively, which supports the suggested assignment of the B state to (2)(2)B1 by Anand et al. based on their experiments. Our CASPT2 Tv and Tv' calculations and our MRCI T0, Tv, and Tv' calculations all indicate that the 2(2)B1 state of C6H5F+ lies below 1(2)B2. By checking the relative energies of the asymptote products and checking the fragmental geometries and the charge and spin density populations in the asymptote products along the CASPT2//CASSCF PECs, we conclude that the 1(2)B1, 1(2)B2, and 1(2)A1 states of C6H5F+ correlate with C6H5+ (1(1)A1) + F (2P) (the first dissociation limit). The energy increases monotonically along the 1(2)B1 PEC, and there are barriers and minima along the 1(2)B2 and 1(2)A1 PECs. The predicted appearance potential value for C6H5+ (1(1)A1) is very close to the average of the experimental values. Our CASPT2//CASSCF PEC calculations have led to the conclusion that the 1(2)A2 state of C6H5F+ correlates with the third dissociation limit of C6H5+ (1(1)A2) + F (2P), and a preliminary discussion is presented.

Diffusion Processes on Power-Law Small-World Networks

We consider diffusion processes on power-law small-world networks in different dimensions. In one dimension, we find a rich phase diagram, with different transient and recurrent phases, including a critical line with continuously varying exponents. The results were obtained using self-consistent perturbation theory and can also be understood in terms of a scaling theory, which provides a general framework for understanding processes on small-world networks with different distributions of long-range links.

The shape of a flexible polymer in a cylindrical pore

We calculate the mean end-to-end distance R of a self-avoiding polymer encapsulated in an infinitely long cylinder with radius D. A self-consistent perturbation theory is used to calculate R as a function of D for impenetrable hard walls and soft walls. In both cases, R obeys the predicted scaling behavior in the limit of large and small D. The crossover from the three-dimensional behavior (D --> infinity) to the fully stretched one-dimensional case (D --> 0) is nonmonotonic. The minimum value of R is found at D approximately 0.46R(F), where R(F) is the Flory radius of R at D --> infinity. The results for soft walls map onto the hard wall case with a larger cylinder radius.

Out-of-Equilibrium Transport Phenomena through a Quantum Dot in a Magnetic Field

We investigate nonequilibrium transport through a dot in a finite magnetic field in a weak correlation regime by using the self-consistent perturbation theory in the Keldysh formalism. Separation of the density of states between the up and down spins becomes smaller gradually and ends up with the Zeeman energy as increasing the bias voltage. Concerning the differential conductance the zero-bias peak splits into two peaks when magnetic field is increased. The critical field for the splitting decreases as the Coulomb interaction is increased.

Calculation of Optical Conductivity of YbB12using Realistic Tight-binding Model

Based on the previously reported tight-binding model fitted to the LDA+U band calculation, optical conductivity of the prototypical Kondo insulator YbB$_{12}$ is calculated theoretically. Many-body effects are taken into account by the self-consistent second order perturbation theory. The gross shape of the optical conductivity observed in experiments are well described by the present calculation, including their temperature-dependences.