The Kondo effect in spin chains

It is well known that the free electron Kondo problem can be described by a one-dimensional (1D) model because only the s-wave part of the electronic wavefunction is affected by the Kondo coupling. Moreover, since only the spin degrees of freedom are involved in the Kondo interaction, and due to spin–charge separation in 1D, the universal low energy long distance physics of the Kondo model also arises when a magnetic impurity is coupled to the end of a gapless antiferromagnetic J1–J2 spin- chain, where J1(J2) is the (next) nearest neighbor coupling. Experimental realizations of such spin chain models are possible and, using various analytical and numerical techniques, we present a detailed and quantitative comparison between the usual free electron Kondo model and such spin chain versions of the Kondo problem. For the gapless J1–J2 spin chain two cases are studied, with zero next nearest neighbor coupling, J2 = 0, and with a critical second-neighbor coupling, J2 = J2c. We first focus on the spin chain impurity model with a critical second-neighbor antiferromagnetic exchange where a bulk marginal coupling present in the spin chain model for J2