Conserving approximations for strongly fluctuating electron systems. I. Formalism and calculational approach

Bickers, N. E.; Scalapino, D. J.

doi:10.1016/0003-4916(89)90359-x

Cited by 426 publications

(457 citation statements)

References 19 publications

Supporting

Mentioning

447

Contrasting

Order By: Relevance

“…TMA is the T -matrix approximation [23]. Finally, FLEX is the fluctuation exchange approximation [21,22].…”

Section: B Weak-coupling Approachesmentioning

confidence: 99%

“…1), which dominate the diagrammatic series when the typical interparticle distance is much larger than the range of the interaction [23]. In the FLEX approach [21,22], finally, bubble, particle-particle, and particle-hole ladder diagrams are included (bottom part of Fig. 1), which means that this approximation treats the interaction of electrons via spin, density, and pairing fluctuations on equal footing.…”

Section: B Weak-coupling Approachesmentioning

confidence: 99%

“…Alternative schemes, such as the combination with the nonlocal self-energy from the fluctuationexchange approximation (FLEX) [21,22] or the T -matrix approximation (TMA) [23], will also be considered in this work. 1 The advantage of an approach which combines DMFT and MBPT at the single-particle (self-energy) level is that the computational effort is comparable to single-site DMFT and that the extension to multiband systems is rather straightforward.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime

Gukelberger

Werner

2015

Phys. Rev. B

View full text Add to dashboard Cite

We study the two-dimensional Hubbard model in the weak-coupling regime and compare the self-energy obtained from various approximate diagrammatic schemes to the result of diagrammatic Monte Carlo simulations, which sum up all weak-coupling diagrams up to a given order. While dynamical mean-field theory provides a good approximation for the local part of the self-energy, including its frequency dependence, the partial summation of bubble and/or ladder diagrams typically yields worse results than second-order perturbation theory. Even widely used self-consistent schemes such as GW or the fluctuation-exchange approximation (FLEX) are found to be unreliable. Combining the dynamical mean-field self-energy with the nonlocal component of GW in GW + DMFT yields improved results for the local self-energy and nonlocal self-energies of the correct order of magnitude, but here, too, a more reliable scheme is obtained by restricting the nonlocal contribution to the second-order diagram. FLEX + DMFT is found to give accurate results in the low-density regime, but even worse results than FLEX near half-filling.

show abstract

“…TMA is the T -matrix approximation [23]. Finally, FLEX is the fluctuation exchange approximation [21,22].…”

Section: B Weak-coupling Approachesmentioning

confidence: 99%

Section: B Weak-coupling Approachesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime

Gukelberger

Werner

2015

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…Semi-analytic approximations such as the iterated perturbation theory (IPT) [31,48,33], the non-crossing approximation (NCA) [33,49], the fluctuation exchange approximation (FLEX) [50][51][52][53], the local moment approach (LMA) [54,55], and the parquet approximation [56] can also provide valuable insight.…”

Section: Solution Of the Self-consistency Equations Of The Dmftmentioning

confidence: 99%

Dynamical Mean-Field Theory

Vollhardt

Byczuk

Kollar

2011

Springer Series in Solid-State Sciences

View full text Add to dashboard Cite

Abstract. The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the foundations of the DMFT, derive the underlying self-consistency equations, and present several applications which have provided important insights into the properties of correlated matter. Motivation Electronic CorrelationsAlready in 1937, at the outset of modern solid state physics, de Boer and Verwey [1] drew attention to the surprising properties of materials with incompletely filled 3d-bands. This observation prompted Mott and Peierls [2] to discuss the interaction between the electrons. Ever since transition metal oxides (TMOs) were investigated intensively [3]. It is now well-known that in many materials with partially filled electron shells, such as the 3d transition metals V and Ni and their oxides, or 4f rare-earth metals such as Ce, electrons occupy narrow orbitals. The spatial confinement enhances the effect of the Coulomb interaction between the electrons, making them "strongly correlated". Correlation effects can lead to profound quantitative and qualitative changes of the physical properties of electronic systems as compared to non-interacting particles. In particular, they often respond very strongly to changes in external parameters. This is expressed by large renormalizations of the response functions of the system, e.g., of the spin susceptibility and the charge compressibility. In particular, the interplay between the spin, charge and orbital degrees of freedom of the correlated d and f electrons and with the lattice degrees of freedom leads to an amazing multitude of ordering phenomena and other fascinating properties, including high temperature superconductivity, colossal magnetoresistance and Mott metal-insulator transitions [3].arXiv:1109.4833v1 [cond-mat.str-el]

show abstract

“…For example new boson fields were suggested to mediate between electrons due to the weakness of the isotope effect in these exotic superconductors. Let us mention plasmons [1,2], spin fluctuations [3,4] or even excitons [5,6]. Especially important is the fact that the critical temperature of cuprates strongly depends on doping and the crystal structure.…”

Section: Introductionmentioning

confidence: 99%

On Some Factors Affecting the Critical Temperature in a Two-Band Model of Superconductivity

Tarasewicz

2013

J Supercond Nov Magn

View full text Add to dashboard Cite

The influence of a few factors on the critical temperature in a two-band superconducting system is investigated. The system contains conventional Cooper pairs from a wider band (the d-band) as well as local pairs (local bipolarons) from a narrower band (the f-band), which are induced via a pair-exchange potential. These factors are the Coulomb repulsion between f-electrons, the position of the f-band with respect to the bottom of the d-band and two kinds of hopping in the f-band: a single-polaron hopping and a pair hopping. The Coulomb potential turns out to lower the critical temperature from higher values to the pure BCS one. Each of the kinds of hopping is treated by making use of perturbation theory. Pair hopping is incorporated as the first order correction but the hopping of single polarons enters as the second order one. Each of them increases this temperature on its own, however, the hopping of single polarons makes it stronger. The position of the f-band that corresponds to the site energy of a f-electron poses a very interesting case. There appear two peaks at two values of that energy meaning a rapid increase of the critical temperature due to the strong effect of the presence of local electron pairs. In this case one has to do with a purely chemical mechanism of the increase of the critical temperature.

show abstract

Conserving approximations for strongly fluctuating electron systems. I. Formalism and calculational approach

Cited by 426 publications

References 19 publications

On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime

On the dangers of partial diagrammatic summations: Benchmarks for the two-dimensional Hubbard model in the weak-coupling regime

Dynamical Mean-Field Theory

On Some Factors Affecting the Critical Temperature in a Two-Band Model of Superconductivity

Contact Info

Product

Resources

About