Scaling Theory of the Asymmetric Anderson Model

1978/02/06 by F. D. M. Haldane · 549 citations
Physics and Astronomy · #Advanced Condensed Matter Physics #Anderson impurity model #Condensed matter physics #Electron #Ground state #Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum mechanics #Scaling #Valence (chemistry)

paper · doi:10.1103/physrevlett.40.416

published in Physical Review Letters 40(6), 416-419 (American Physical Society)

openalex publication_date 1978/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A scaling theory is used to show that for temperatures T\ensuremath≪U, the properties of the asymmetric Anderson model (U\ensuremath≫|E_d|, \ensuremathΔ) are universal functions of the scaling invariants \ensuremathΔ and E_d^*=E_d+(\frac\ensuremathΔ\ensuremathπ)ln(\fracW₀\ensuremathΔ), where W₀ is the conduction electron bandwidth or U, whichever is smaller. Crossovers between various regimes of simple behavior as the temperature changes are described. |E_d^*|\ensuremath\lesssim\ensuremathΔ is identified as the criterion for a "mixed-valence" ground state, where the susceptibility \ensuremath≈\ensuremathΔ^\ensuremath-1. For \ensuremath-E_d^*\ensuremath≫\ensuremathΔ, there is a local-moment regime with a Kondo temperature T_K\ensuremath≈\ensuremathΔexp(\frac\ensuremathπE_d^*2\ensuremathΔ).

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