Migdal’s theorem and the pseudogap

Monthoux, P.

doi:10.1103/physrevb.68.064408

Cited by 18 publications

(47 citation statements)

References 46 publications

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“…Violations of this theorem appear if the magnon frequency becomes large 12,13 or non-adiabaticity leading eventually to a polaron collapse 14 . For heavy fermion systems the Migdal theorem is not valid 15 and near the magnetic boundary the quasiparticle spectra is different from the Eliashberg theory 16 which means the applicability of RPA calculations in high-T c superconductivity 17,18 is questionable.…”

Section: Pacs Numbersmentioning

confidence: 99%

Conditions where random phase approximation becomes exact in the high-density limit

Morawetz

Ashokan

Bala³

et al. 2018

Phys. Rev. B

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It is shown that in d-dimensional systems, the vertex corrections beyond the random phase approximation (RPA) or GW approximation scales with the power d − β − α of the Fermi momentum if the relation between Fermi energy and Fermi momentum is ǫ f ∼ p β f and the interacting potential possesses a momentum-power-law of ∼ p −α . The condition d − β − α < 0 specifies systems where RPA is exact in the high-density limit. The one-dimensional structure factor is found to be the interaction-free one in the high-density limit for contact interaction. A cancellation of RPA and vertex corrections render this result valid up to second-order in contact interaction. For finite-range potentials of cylindrical wires a large-scale cancellation appears and found to be independent of the width parameter of the wire. The proposed high-density expansion agrees with the Quantum Monte Carlo simulations. PACS numbers:The correlation energy in electron gases has been a topic of long-time investigations. In order to avoid divergences in perturbation theory already Macke 1 summed an infinite series of diagrams (RPA). Later Gell-Man and Bruckner show that the RPA at zero temperature becomes exact in the high-density limit 2,3 confirmed up to orders of the logarithm of density 4 . The corresponding momentum distributions in RPA have been computed already in 5,6 and recently an improved parametrization has been presented by cummulant expansions 7 . It confirms that the high-density limit is indeed given by the RPA calculation. The analytic expressions of the electron gas have been found 8,9 and an approximation bridging the low and high-density expansion of the correlation energy has been provided 10 .The Migdal theorem 11 contains a similar statement that for an electron-phonon coupling, higher-order vertex corrections vanish in orders of the ratio of the phonon frequency to the Fermi energy. Violations of this theorem appear if the magnon frequency becomes large 12,13 or non-adiabaticity leading eventually to a polaron collapse 14 . For heavy fermion systems the Migdal theorem is not valid 15 and near the magnetic boundary the quasiparticle spectra is different from the Eliashberg theory 16 which means the applicability of RPA calculations in high-T c superconductivity 17,18 is questionable.It is therefore desirable to have a simple criterion when vertex corrections vanish in the high-density limit. Here we provide an argument from simple scaling for interacting Fermi systems which shows that the power exponent of the interaction and the dimensionality of the system together with the exponent of the relation between Fermi energy and momentum, determines the expansion of the vertex corrections in terms of the Fermi momentum. First we drive an exact scaling law combining the dimensionality, the form of Fermi energy, and the momentum behavior of the potential into a condition when RPA is exact. As an application, we calculate the structure factor and pair correlation function for a wire of Fermions and compare the result with recent Quantum Mo...

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Section: Pacs Numbersmentioning

confidence: 99%

Conditions where random phase approximation becomes exact in the high-density limit

Morawetz

Ashokan

Bala³

et al. 2018

Phys. Rev. B

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“…[14]). Although the quasistatic approach was applied previously to systems in the vicinity of a FM instability [20], only the form of spectral functions was analyzed, the self-energy, magnetic and triplet pairing susceptibilities being not investigated.…”

Section: Introductionmentioning

confidence: 99%

Electronic self-energy and triplet pairing fluctuations in the vicinity of a ferromagnetic instability in two-dimensional systems: Quasistatic approach

Катанин

2005

Phys. Rev. B

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The self-energy, spectral functions and susceptibilities of 2D systems with strong ferromagnetic fluctuations are considered within the quasistatic approach. The self-energy at low temperatures T has a non-Fermi liquid form in the energy window |ω| ∆0 near the Fermi level, where ∆0 is the groundstate spin splitting for magnetically ordered ground state, and ∆0 ∝ T 1/2 ln 1/2 (vF /T ) in the quantum critical regime (vF is the Fermi velocity). Spectral functions have a two-peak structure at finite T above the magnetically ordered ground state, which implies quasi-splitting of the Fermi surface in the paramagnetic phase in the presence of strong ferromagnetic fluctuations. The triplet pairing amplitude in the quasistatic approximation increases with increasing correlation length; at low temperatures T ≪ ∆0 the vertex corrections become important and the Eliashberg approach is not justified. The results for the spectral properties and susceptibilities in the quantum critical regime near charge-(spin-) instabilities with large enough correlation length ξ ≫ (T /vF ) −1/3 are obtained.

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“…A Monte Carlo simulation is a method of use, as has been performed for the phenomenological model with spin fluctuation and that with charge fluctuation. 86 However, we carry out an approximate but analytic treatment in order to obtain a clearer understanding and to compare several approximations in an equal footing.…”

Section: Magnetic Propertiesmentioning

confidence: 99%

Pseudogap and Superconducting Fluctuation in High-T_cCuprates: Theory beyond 1-Loop Approximation

Yanase

2004

J. Phys. Soc. Jpn.

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The pseudogap phenomena induced by the SC fluctuation are investigated in details. We perform a calculation beyond the 1-loop approximation. The SC fluctuation is microscopically derived on the basis of the repulsive Hubbard model. The vertex corrections are collected in the infinite order with use of the quasi-static approximation. The single-particle excitations, NMR 1/T1T , spin susceptibility and superconducting transition temperature are discussed. The important role of the vertex correction is pointed out for the single particle spectral function. On the other hand, the validity of the 1-loop order theory is confirmed for other quantities. We shed light on the essential nature of SC fluctuation leading to the pseudogap from the comparison with spin and charge fluctuations.

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Migdal’s theorem and the pseudogap

Cited by 18 publications

References 46 publications

Conditions where random phase approximation becomes exact in the high-density limit

Conditions where random phase approximation becomes exact in the high-density limit

Electronic self-energy and triplet pairing fluctuations in the vicinity of a ferromagnetic instability in two-dimensional systems: Quasistatic approach

Pseudogap and Superconducting Fluctuation in High-T_cCuprates: Theory beyond 1-Loop Approximation

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Migdal’s theorem and the pseudogap

Cited by 18 publications

References 46 publications

Conditions where random phase approximation becomes exact in the high-density limit

Conditions where random phase approximation becomes exact in the high-density limit

Electronic self-energy and triplet pairing fluctuations in the vicinity of a ferromagnetic instability in two-dimensional systems: Quasistatic approach

Pseudogap and Superconducting Fluctuation in High-TcCuprates: Theory beyond 1-Loop Approximation

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Pseudogap and Superconducting Fluctuation in High-T_cCuprates: Theory beyond 1-Loop Approximation