An integrable Kondo problem in the one-dimensional supersymmetric extended Hubbard model is studied by means of the boundary graded quantum inverse scattering method. The boundary K -matrices depending on the local moments of the impurities are presented as a non-trivial realization of the graded reflection equation algebras in a two-dimensional impurity Hilbert space. Further, the model is solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained.

arXiv:cond-mat/9811048Journal of Physics A Mathematical and GeneralJan 1, 19995 citations

arXiv:0911.2858 · Annals of Physics

A Lie algebraic approach to the Kondo problem

S. G. Rajeev

Published Jan 19, 2010• 1 citation

arXiv HTML PDF

DOI: 10.1016/j.aop.2010.01.004

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We study Kondo physics in the algebraic spin liquid, recently proposed to describe

ZnCu_{3}(OH)_{6}Cl_{2}

[Phys. Rev. Lett. {\bf 98}, 117205 (2007)]. Although spin dynamics of the algebraic spin liquid is described by massless Dirac fermions, this problem differs from the Pseudogap Kondo model, because the bulk physics in the algebraic spin liquid is governed by an interacting fixed point where well-defined quasiparticle excitations are not allowed. Considering an effective bulk model characterized by an anomalous critical exponent, we derive an effective impurity action in the slave-boson context. Performing the large-

N_σ

analysis with a spin index

N_σ

, we find an impurity quantum phase transition from a decoupled local-moment state to a Kondo-screened phase. We evaluate the impurity spin susceptibility and specific heat coefficient at zero temperature, and find that such responses follow power-law dependencies due to the anomalous exponent of the algebraic spin liquid. Our main finding is that the Wilson's ratio for the magnetic impurity depends strongly on the critical exponent in the zero temperature limit. We propose that the Wilson's ratio for the magnetic impurity may be one possible probe to reveal criticality of the bulk system.