The two-impurity, two-channel Kondo problem: A conformal field theory approach.

摘要

We study the Kondo interaction of two spin 1/2 impurities with two degenerate partial-wave channels of electrons. The competition between the Kondo screening of the impurity spins and the RKKY interaction between them results in a complex Renormalization Group (RG) diagram, which reveals a one-parameter family of fixed points.; We solve the theory when the model is symmetric under the exchange of even and odd-parity fermion species, and show that it always has a completely marginal operator, whose insertion as a Hamiltonian deformation "rotates" the boundary state of the Conformal Field Theory description, and is responsible for the aforementioned line of fixed points. We describe in detail the nature of the non-Fermi-liquid fixed points, whose (untwisted) boundary operators in general have scaling dimensions that depend continuously on the Lagrangian coupling of the marginal deformation. We pay special attention to the {dollar}Zsb2{dollar} orbifold points, which exhibit a very rich algebraic structure, with connections to Supersymmetry and {dollar}{lcub}cal W{rcub}{dollar}-algebras.; We present preliminary results that extend this study to the region of the RG diagram which is not symmetric under the exchange of even and odd electrons. This results in another {dollar}Zsb2{dollar} orbifold of central charge c = 1. We provide the appropriate conformal embedding of the non-interacting theory that is relevant for the discussion of the additional interaction.; Finally, we examine more than one hundred energy levels of Numerical Renormalization Group data at each of four different fixed points, and show their excellent agreement with our predictions.