Quantum replica approach to the under-screened Kondo model

TL;DR

This paper introduces a novel large N approach to the underscreened Kondo model that accurately captures the finite phase shift and energy dependence of the singular Fermi liquid state, using a flavor quantum number in the Schwinger boson framework.

Contribution

It develops a new large N method that models the full energy dependence of the underscreened Kondo model without explicit spin constraints, capturing key physical features.

Findings

Successfully models the energy dependence of the Abrikosov Suhl resonance.

Accurately describes the finite elastic phase shift in the singular Fermi liquid.

Provides a field-dependent magnetization profile consistent with the 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.