Quantum replica approach to the underscreened Kondo model

P. Coleman and I. Paul
Phys. Rev. B 71, 035111 – Published 24 January 2005

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=KN 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 NK 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 KN 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.

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  • Received 14 June 2004

DOI:https://doi.org/10.1103/PhysRevB.71.035111

©2005 American Physical Society

Authors & Affiliations

P. Coleman1 and I. Paul2

  • 1Center for Materials Theory, Rutgers University, Piscataway, New Jersey 08855, USA
  • 2SPhT, L’Orme des Merisiers, CEA-Saclay, 91191 Gif-sur-Yvette, France

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Vol. 71, Iss. 3 — 15 January 2005

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