Quantum replica approach to the under-screened Kondo model

Abstract

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-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 underscreened Kondo model and the field-dependent magnetization.

Revised draft, with plots explicitly showing logarithmic scaling of inverse coupling constant. Small corrections prior to submission to journal

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• Model for Ferromagnetic Quantum Critical Point in a 1D Kondo Lattice
• Schwinger Boson approach to the fully screened Kondo model
• Application of the S=1 underscreened Anderson lattice model to Kondo uranium and neptunium compounds
• Conductance of a spin-1 quantum dot: the two-stage Kondo effect
• Quantum phase transition in a two-dimensional Kondo-Heisenberg model: a Schwinger-boson large-N approach
• Analysis of the Kondo effect in ferromagnetic atomic-sized contacts
• Fermi liquid identities for the Infinite U Anderson Model
• Interplay of charge and spin fluctuations in a Hund's coupled impurity