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Quantum replica approach to the underscreened Kondo model

2005; American Physical Society; Volume: 71; Issue: 3 Linguagem: Inglês

10.1103/physrevb.71.035111

1550-235X

Piers Coleman, I. Paul,

Iron-based superconductors research

We extend the Schwinger boson large $N$ treatment of the underscreened Kondo model in a way that correctly captures the finite elastic phase shift in the singular Fermi liquid. The new feature of the approach is the introduction of a flavor quantum number with $K$ possible values associated with the Schwinger boson representation. The large $N$ limit is taken maintaining the ratio $k=K∕N$ fixed. This approach differs from previous approaches in that we do not explicitly enforce a constraint on the spin representation of the Schwinger bosons. Instead, the energetics of the Kondo model cause the bosonic degrees of freedom to ``self-assemble'' into a ground-state in which the spins of $K$ bosons and $N\ensuremath{-}K$ conduction electrons are antisymmetrically arranged into a Kondo singlet. With this device the large $N$ limit can be taken in such a way that a fraction $K∕N$ of the Abrikosov-Suhl resonance is immersed inside the Fermi sea. We show how this method can be used to model the full energy dependence of the singular Abrikosov-Suhl resonance in the under-screened Kondo model and the field-dependent magnetization.