<i>The Theory of Interacting Fermi Systems</i>

Nozières, P.; Hone, Daniel; Rose, M. E.

doi:10.1063/1.3051704

Cited by 214 publications

(294 citation statements)

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“…(61) is proved identically. Note that the contribution from (ii) vanishes after all [17]. In the same way, we can derive the Ward identities for ∂ α Λ ν (k; k) ≡ Λ ν,α and ∂ αβ Λ ν (k; k) ≡ Λ ν,αβ , which are expressed as Fig.17.…”

Section: Magnetoconductivity: With Full Vertex Correctionsmentioning

confidence: 99%

“…This fact brings the divergence of the static conductivities σ xx , ∆σ xy and ∆σ xx even at finite temperatures, reflecting the momentum conservation law. On the other hand, J (2) µ (k, ǫ; ω) gives the total current with the 'backflow' in the case of γ * k ≪ ω ≪ T , or in the 'zero-sound regime' [17,18]. In this case J k is finite.…”

Section: A the Role Of The Vertex Correctionsmentioning

confidence: 99%

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General formula for the magnetoresistance on the basis of Fermi liquid theory

Kontani

2001

Phys. Rev. B

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The general expression for the magnetoresistance (MR) due to the Lorentz force is derived by using the Fermi liquid transport theory based on the Kubo formula. The obtained gauge-invariant expression is exact for any strength of the interaction, as for the most singular term with respect to 1/γ * k (γ * k being the quasiparticle damping rate). By virtue of the exactness, the conserving laws are satisfied rigorously in the present expression, which is indispensable for avoiding unphysical solutions. Based on the derived expression, we can calculate the MR within the framework of the Baym-Kadanoff type conserving approximation, by including all the vertex corrections required by the Ward identity. The present expression is significant especially for strongly correlated systems because the current vertex corrections will be much important. On the other hand, if we drop all the vertex corrections in the formula, we get the MR of the relaxation time approximation (RTA), which is commonly used because of the simplicity. However, the RTA is dangerous because it may give unphysical results owing to the lack of conserving laws. In conclusion, the present work enables us to study the MR with satisfying the conserving laws which is highly demanded in strongly correlated electrons, such as high-Tc superconductors, organic metals, and heavy Fermion systems. In Appendix D, we reply to the comment by O. Narikiyo [cond-mat/0006028]. (Note that Appendix D exists only in the e-preprint version.)

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Section: Magnetoconductivity: With Full Vertex Correctionsmentioning

confidence: 99%

Section: A the Role Of The Vertex Correctionsmentioning

confidence: 99%

General formula for the magnetoresistance on the basis of Fermi liquid theory

Kontani

2001

Phys. Rev. B

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“…A(P ) = ±1 for a skelton diagram, and A(P ) = 0 for others. U (k 1 , k 2 |k 3 , k 4 ) is the two-body interaction where k 1 , k 3 are incoming and k 2 , k 3 are outgoing, respectively [27,35]. Here we consider the on-site Coulomb interaction: U (k 1 , k 2 |k 3 , k 4 ) = U δ k1+k3,k2+k4 δ ǫ1+ǫ3,ǫ2+ǫ4 δ σ1,σ2 δ σ3,σ4 δ α1,−σ3 .…”

Section: Appendix A: Another Derivation Of the Heat Current Operatormentioning

confidence: 99%

“…In general, T 2i is well approximated at lower temperatures as (T 1i + T 3i )/2 [6]. Thus, taking the Ward identity for electron current is taken into account [26,27],…”

Section: Linear Response Theory For S and κmentioning

confidence: 99%

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General formula for the thermoelectric transport phenomena based on Fermi liquid theory: Thermoelectric power, Nernst coefficient, and thermal conductivity

Kontani

2003

Phys. Rev. B

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On the basis of the linear response transport theory, the general expressions for the thermoelectric transport coefficients, such as thermoelectric power (S), Nernst coefficient (ν), and Thermal conductivity (κ), are derived by using the Fermi liquid theory. The obtained expression is exact as for the most singular term in terms of 1/γ * k (γ * k being the quasiparticle damping rate). We utilize the Ward identities for the heat velocity which is derived by the local energy conservation law. The derived expressions enable us to calculate various thermoelectric transport coefficients in a systematic way, within the framework of the conserving approximation as Baym and Kadanoff. Thus, the present expressions are very useful for studying the strongly correlated electrons such as high-Tc superconductors, organic metals, and heavy Fermion systems, where the current vertex correction (VC) is expected to play important roles. By using the derived expression, we calculate the thermal conductivity κ in a free-dispersion model up to the second-order with respect to the on-site Coulomb potential U . We find that it is slightly enhanced due to the VC for the heat current, although the VC for electron current makes the conductivity (σ) of this system diverge, reflecting the absence of the Umklapp process.

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Weakly interacting electrons and the renormalization group

2003

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We present a general method to study weak-coupling instabilities of a large class of interacting electron models in a controlled and unbiased way. Quite generally, the electron gas is unstable towards a superconducting state even in the absence of phonons, since high-energy spin fluctuations create an effective attraction between the quasi-particles. As an example, we show the occurrence of d-wave pairing in the repulsive Hubbard model in two dimensions. In one dimension or if the Fermi surface is nested, there are several competing instabilities. The required renormalization group formalism for this case is presented to lowest (one-loop) order on a most elementary level, connecting the idea of the ``parquet summation'' to the more modern concept of Wilson's effective action. The validity and restrictions of the one-loop approximation are discussed in detail. As a result, three different renormalization group approaches known in the literature are shown to be equivalent within the regime of applicability. We also briefly discuss the open problem of a two-dimensional Fermi system at Van Hove filling without nesting.Comment: 33 pages, 15 figures, minor correction

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The Theory of Interacting Fermi Systems

Cited by 214 publications

References 0 publications

General formula for the magnetoresistance on the basis of Fermi liquid theory

General formula for the magnetoresistance on the basis of Fermi liquid theory

General formula for the thermoelectric transport phenomena based on Fermi liquid theory: Thermoelectric power, Nernst coefficient, and thermal conductivity

Weakly interacting electrons and the renormalization group

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