Quantum Field Theoretical Methods in Statistical Physics

Абрикосов, А. А.; Gor’kov, L. P.; Dzyaloshinskii, I. Ye.; Corngold, Noel

doi:10.1119/1.1974503

Cited by 586 publications

(812 citation statements)

References 0 publications

Supporting

Mentioning

796

Contrasting

Unclassified

Order By: Relevance

“…(18). It is worth noting that such obtained spectral function (20) satisfies the normalization condition ∞ −∞ dωA(kω) = 1 with an accuracy better than 0.01.…”

Section: Spectral Functionmentioning

confidence: 99%

“…(20) when a frequency satisfying the equation 1 − t k ℜK(ω) = 0 falls into a region of a small damping |ℑK(ω)| and due to the strong frequency dependence of ℑK(ω) in the numerator of Eq. (20). The high-frequency bands and the low-frequency bands in the central part and at the periphery of the Brillouin zone arise due to the first reason.…”

Section: Spectral Functionmentioning

confidence: 99%

“…They are located in the same frequency ranges as the low-frequency maxima originated from the resonance denominator in Eq. (20). Therefore they can be combined in a common dispersion band, although widths of the maxima of different origin can significantly vary for a smaller artificial broadening.…”

Section: Spectral Functionmentioning

confidence: 99%

“…The change to real frequencies carried out in the previous section converts the Matsubara function (2) into the retarded Green's function. 20 It is an analytic function in the upper half-plane which requires that ℑK(ω) be negative. As seen from Fig.…”

Section: Fig 1: Diagrams Of the First Four Orders Of Expansion (4)mentioning

confidence: 99%

See 3 more Smart Citations

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

“…(18). It is worth noting that such obtained spectral function (20) satisfies the normalization condition ∞ −∞ dωA(kω) = 1 with an accuracy better than 0.01.…”

Section: Spectral Functionmentioning

confidence: 99%

Section: Spectral Functionmentioning

confidence: 99%

Section: Spectral Functionmentioning

confidence: 99%

Section: Fig 1: Diagrams Of the First Four Orders Of Expansion (4)mentioning

confidence: 99%

See 2 more Smart Citations

One-loop approximation for the Hubbard model

Sherman

2007

Physica C: Superconductivity

View full text Add to dashboard Cite

show abstract

“…Here we mention the relation with the entropy s [12], assuming the low-T form as follows from the FL theory [16], i.e. s = π 2 T N (µ)/3Z.…”

mentioning

confidence: 99%

Spectral properties of the planar t-J model

Prelovšek

Jaklič

1997

Physica C: Superconductivity

View full text Add to dashboard Cite

The single-particle spectral functions A(k, ω) and self-energies Σ(k, ω) are calculated within the t−J model using the finite-temperature Lanczos method for small systems. A remarkable asymmetry between the electron and hole part is found. The hole (photoemission) spectra are overdamped, with ImΣ ∝ ω in a wide energy range, consistent with the marginal Fermi liquid scenario, and in good agreement with experiments on cuprates. In contrast, the quasiparticles in the electron part of the spectrum show weak damping.PACS numbers: 71.27.+a, 79.60.-i, 71.20.-b The normal state of superconducting cuprates in many aspects contradicts the phenomenology of the normal Fermi liquid (FL). Anomalous frequency and temperature dependence of several response functions is generally attributed to electronic correlations, yet a proper description is missing so far. The angle resolved photoemission (ARPES) experiments [1-3] probe the one-particle spectral function A(k, ω). At intermediate doping they reveal for a wide class of cuprates a well defined large Fermi surface (FS) consistent with the Luttinger theorem and similar quasiparticle (QP) dispersion [2]. This seems to imply the validity of the concept of the usual metal with electronic-like FS. Such simple FL picture is in an apparent contradiction with magnetic and transport properties, e.g. electrical conductivity scales with hole concentration, closer to the picture of holes moving in the antiferromagnetic (AFM) background. Moreover, in ARPES the FL interpretation is spoiled by the overdamped character of QP peaks [3,2]. Although a large background makes fits of particular lineshapes non-unique [3,4], the QP inverse lifetime is found to be of the order of the QP energy, i.e. τ −1 ∝ ω for ω > T , leading to the concept of the marginal Fermi liquid (MFL) [5] with an anomalous single-particle and transport relaxation, in contrast to τ −1 ∝ ω 2 in the normal FL.It is unclear whether above features can be reproduced within generic models of strongly correlated systems, such as the Hubbard and the t − J model, in particular in the most challenging regime of intermediate doping. Spectral properties of these 2D models have been so far studied mainly via numerical techniques [6], e.g. exact diagonalization (ED) [7] and Quantum Monte Carlo (QMC) [8]. These studies, as well as some analytical approaches [9], established a reasonable consistency of the model QP dispersion with the experimental one, as well as the possibility of large FS, but have not been able to investigate closer the character of QP, being in the core of the anomalous low-energy properties.The aim of the present work is to employ the finitetemperature Lanczos method [10] to calculate A(k, ω) within the t − J model. This method has been already applied to other dynamic [11] and static [12] functions, yielding features consistent with the MFL concept and experiments on cuprates. Although calculations are still done in small systems, by using finite (but small) T > 0 smooth enough spectra are obtained not only to determ...

show abstract

Renormalized Perturbation Expansion in Kinetic Theory

Der

1977

Annalen der Physik

View full text Add to dashboard Cite

Ladder summation techniques are applied to the recently developed c-number diagram expansion for kinetic equations describing the relaxation of quantum fluids. By way of the resummation, the kinetic equations are reformulated in terms of a T-matrix which describes the scattering of two particles influenced by the remaining particles of the system via the particle statistics (Bose or Fermi). At sufficiently high temperatures (Maxwell-Boltzmann statistics), the Tmatrix introduced coincides with the usual T-matrix of conventional two-body scattering theory in free space. In low-temperature Fermi systems, the T-matrix differs from the reaction matrix of the Brueckner-Goldstone theory because the "healing" property of the two-body wave function does not obtain. Renormalisierte Entwicklungen in Storungsrechnungen der kinetischen TheorieI n h a l tsubersicht. Fur die Beschreibung von Relaxationsprozessen in Quantenfluiden wurden in einer fruheren Arbeit kinetische Gleichungen abgeleitet, die mittels Graphenentwicklungen formuliert sind. In der vorliegenden Arbeit wird durch Aufsummation der Zweiteilchenleiter eine T-Matrix eingefuhrt, die die Streuung zweier Teilchen unter dem EinfluS der ubrigen Teilchen durch die Teilchenstatistik (Bose oder Fermi) beschreibt. Bei hinreichend hohen Temperaturen (Maxwell-Boltzmann-Statistik) geht die eingefuhrte 5"-Matrix in die ubliche T-Matrix der Zweiteilchenstreutheorie im freien Raum uber. Fur Fermisysteme bei niedrigen Temperaturen unterscheidet sich die T-Matrix von der Reaktionsmatrix der Brueckner-Goldstone-Theorie, weil die Zweiteilchenwellenfunktion nicht ,,heilt".

show abstract

Quantum Field Theoretical Methods in Statistical Physics

Cited by 586 publications

References 0 publications

One-loop approximation for the Hubbard model

One-loop approximation for the Hubbard model

Spectral properties of the planar t-J model

Renormalized Perturbation Expansion in Kinetic Theory

Contact Info

Product

Resources

About