Higher-order Fermi-liquid corrections for an Anderson impurity away from half-filling II: equilibrium properties
| Autor: | Alex C. Hewson, Akira Oguri |
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| Rok vydání: | 2017 |
| Předmět: |
FOS: Physical sciences
02 engineering and technology Correlation function (quantum field theory) 01 natural sciences Omega symbols.namesake Condensed Matter - Strongly Correlated Electrons PERTURBATION EXPANSION Impurity 0103 physical sciences Mesoscale and Nanoscale Physics (cond-mat.mes-hall) Feynman diagram 010306 general physics Mathematical physics Physics Science & Technology Condensed Matter - Mesoscale and Nanoscale Physics Strongly Correlated Electrons (cond-mat.str-el) Vertex function Order (ring theory) KONDO PROBLEM 021001 nanoscience & nanotechnology MODEL Physics Condensed Matter Physical Sciences symbols STATIC PROPERTIES Condensed Matter::Strongly Correlated Electrons Fermi liquid theory 0210 nano-technology Energy (signal processing) SYSTEM RENORMALIZATION-GROUP APPROACH DILUTE MAGNETIC-ALLOYS |
| DOI: | 10.48550/arxiv.1710.02948 |
| Popis: | We study the low-energy behavior of the vertex function of a single Anderson impurity away from half-filling for finite magnetic fields, using the Ward identities with careful consideration of the anti-symmetry and analytic properties. The asymptotic form of the vertex function $\Gamma_{\sigma\sigma';\sigma'\sigma}^{}(i\omega,i\omega';i\omega',i\omega)$ is determined up to terms of linear order with respect to the two frequencies $\omega$ and $\omega'$, as well as the $\omega^2$ contribution for anti-parallel spins $\sigma'\neq \sigma$ at $\omega'=0$. From these results, we also obtain a series of the Fermi-liquid relations beyond those of Yamada-Yosida. The $\omega^2$ real part of the self-energy $\Sigma_{\sigma}^{}(i\omega)$ is shown to be expressed in terms of the double derivative $\partial^2\Sigma_{\sigma}^{}(0)/\partial \epsilon_{d\sigma}^{2}$ with respect to the impurity energy level $\epsilon_{d\sigma}^{}$, and agrees with the formula obtained recently by Filippone, Moca, von Delft, and Mora in the Nozi\`{e}res phenomenological Fermi-liquid theory [Phys.\ Rev.\ B {\bf 95}, 165404 (2017)]. We also calculate the $T^2$ correction of the self-energy, and find that the real part can be expressed in terms of the three-body correlation function $\chi_{\uparrow\downarrow,-\sigma}^{[3]} = \partial \chi_{\uparrow\downarrow}/\partial \epsilon_{d,-\sigma}^{}$. We also provide an alternative derivation of the asymptotic form of the vertex function. Specifically, we calculate the skeleton diagrams for the vertex function $\Gamma_{\sigma\sigma;\sigma\sigma}^{}(i\omega,0;0,i\omega)$ for parallel spins up to order $U^4$ in the Coulomb repulsion $U$. It directly clarifies the fact that the analytic components of order $\omega$ vanish as a result of the cancellation of four related Feynman diagrams which are related to each other through the anti-symmetry operation. Comment: 15 figures, 19pages, and supplemental material (15 pages), typo found in (6.15) has been corrected |
| Databáze: | OpenAIRE |
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