Many-body theory versus simulations for the pseudogap in the Hubbard model

Moukouri, S.; Allen, S.; Lemay, Frédéric; Kyung, Bumsoo; Poulin, David; Vilk, Y. M.; Tremblay, A.–M. S.

doi:10.1103/physrevb.61.7887

Cited by 80 publications

(163 citation statements)

References 24 publications

Supporting

Mentioning

152

Contrasting

Order By: Relevance

“…8 enhances the magnetic interaction [14] The most important feature of the calculations presented here is the qualitative change in the quasiparticle spectral function that occurs as the magnetic interaction gets stronger, either on the border of long-range antiferromagnetic or ferromagnetic order. The appearance of a pseudogap in the quasiparticle spectrum near a second-order phase transition as the temperature approaches the critical transition temperature from above was demonstrated for the half-filled Hubbard model [17][18][19], for a superconducting instability [18,[20][21][22][23]33,34] and for a Peierls-CDW transition [32]. By contrast, in the model studied in this paper, the quadratic actions of the dynamical molecular fields do not exhibit a phase transition at all (with κ 2 > 0).…”

Section: Discussionmentioning

confidence: 78%

“…In the half-filled Hubbard model studied in Refs. [17][18][19], the renormalized classical regime for the spin-fluctuations always precedes the zero temperature phase transition, and in that regime thermal fluctuations dominate and the relevant charactersitic length scale is the thermal quasiparticle de Broglie wavelength ξ th = v F /T [17][18][19]. Thermal fluctuations are dominant near the Peierls-CDW transition in two dimensions and the relevant quasiparticle length scale for the onset of the pseudogap also turns out to be ξ th [32].…”

Section: Discussionmentioning

confidence: 99%

“…The validity of Baym-Kadanoff many-body theories such as the fluctuation exchange approximation [16], which is in many ways similar to the Eliashberg theory of the magnetic interaction model, has been extensively studied by Tremblay and collaborators in the context of the Hubbard model [17][18][19]. They find that close to the magnetic boundary, Migdal's theorem qualitatively breaks down, in that a critical-fluctuation-induced pseudogap (or precursor pseudogap) is observed in the Quantum Monte Carlo simulations but is not found in the fluctuation exchange approximation.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Migdal’s theorem and the pseudogap

Monthoux¹

2003

Phys. Rev. B

View full text Add to dashboard Cite

We study a model of quasiparticles on a two-dimensional square lattice coupled to Gaussian distributed dynamical molecular fields. We consider two types of such fields, a vector molecular field that couples to the quasiparticle spin-density and a scalar field coupled to the quasiparticle number density. An important feature of the magnetic pseudogap found in the present calculations is that it is strongly anisotropic. It vanishes along the diagonal of the Brillouin zone and is large near the zone boundary. In the case of ferromagnetic fluctuations, we also find a range of model parameters with qualitative changes in the quasiparticle spectral function not captured by the one-loop approximation, in that the quasiparticle peak splits into two. We find that one needs to be closer to the magnetic boundary to observe the pseudogap effects in the nearly ferromagnetic case relative to the nearly antiferromagnetic one, under otherwise similar conditions. We provide intuitive arguments to explain the physical origin of the breakdown of Migdal's theorem.

show abstract

Section: Discussionmentioning

confidence: 78%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Migdal’s theorem and the pseudogap

Monthoux¹

2003

Phys. Rev. B

View full text Add to dashboard Cite

show abstract

“…It has been benchmarked on Quantum Monte Carlo calculations on the Hubbard model. 33,[43][44][45][46][47] . TPSC has been shown to be in the N = ∞ universality class of the O(N ) model 48 .…”

Section: Finite Temperature Results and Tpscmentioning

confidence: 99%

Breakdown of Fermi liquid behavior at the(π,π)=2kFspin-density wave quantum-critical point: The case of electron-doped cuprates

et al. 2012

Self Cite

View full text Add to dashboard Cite

Many correlated materials display a quantum critical point between a paramagnetic and a spindensity wave (SDW) state. The SDW wave vector connects points, so-called hot spots, on opposite sides of the Fermi surface. The Fermi velocities at these pairs of points are in general not parallel. Here we consider the case where pairs of hot spots coalesce, and the wave vector (π, π) of the SDW connects hot spots with parallel Fermi velocities. Using the specific example of electron-doped cuprates, we first show that Kanamori screening and generic features of the Lindhard function make this case experimentally relevant. The temperature dependence of the correlation length, the spin susceptibility and the self-energy at the hot spots are found using the Two-Particle-SelfConsistent theory and specific numerical examples worked out for band and interaction parameters characteristic of the electron-doped cuprates. While the curvature of the Fermi surface at the hot spots leads to deviations from perfect nesting, the pseudo-nesting conditions lead to drastic modifications of the temperature dependence of these physical observables: Neglecting logarithmic corrections, the correlation length ξ scales like 1/T , namely z = 1 instead of the naive z = 2, the (π, π) static spin susceptibility χ like 1/ √ T , and the imaginary part of the self-energy at the hot spots like T 3/2 . The correction T −1 1 ∼ T 3/2 to the Korringa NMR relaxation rate is subdominant. We also consider this problem at zero temperature, or for frequencies larger than temperature, using a field-theoretical model of gapless collective bosonic modes (SDW fluctuations) interacting with fermions. The imaginary part of the retarded fermionic self-energy close to the hot spots scales as −ω 3/2 log ω. This is less singular than earlier predictions of the form −ω log ω. The difference arises from the effects of umklapp terms that were not included in previous studies.

show abstract

“…3 the intensity of maximum at a positive frequency is larger than in the respective spectrum in Ref. 22 …”

Section: Spectral Functionmentioning

confidence: 99%

One-loop approximation for the Hubbard model

Sherman

2007

Physica C: Superconductivity

View full text Add to dashboard Cite

The diagram technique for the one-band Hubbard model is formulated for the case of moderate to strong Hubbard repulsion. The expansion in powers of the hopping constant is expressed in terms of site cumulants of electron creation and annihilation operators. For Green's function an equation of the Larkin type is derived and solved in a one-loop approximation for the case of two dimensions, nearest-neighbor hopping and half-filling. The obtained four-band structure of the spectrum and the shapes of the spectral function are close to those observed in Monte Carlo calculations. It is shown that the maxima forming the bands are of a dissimilar origin in different regions of the Brillouin zone.

show abstract

Many-body theory versus simulations for the pseudogap in the Hubbard model

Cited by 80 publications

References 24 publications

Migdal’s theorem and the pseudogap

Migdal’s theorem and the pseudogap

Breakdown of Fermi liquid behavior at the(π,π)=2kFspin-density wave quantum-critical point: The case of electron-doped cuprates

One-loop approximation for the Hubbard model

Contact Info

Product

Resources

About