Exotic Kondo effect in two one-dimensional spin-1/2 chains coupled to two localized spin-1/2 magnets

We study an exotic Kondo effect in a system consisting of two one-dimensional XX Heisenberg ferromagnetic spin-1/2 chains (denoted by alpha = u , d for up and down chains) coupled to a quantum dot consisting of two localized spin-1/2 magnets. Using the Jordan-Wigner transformation on the Heisenberg Hamiltonian of the two chains, this system can be expressed in terms of non-interacting spinless fermionic quasiparticles. As a result, the Hamiltonian of the whole system is expressed as an Anderson model for spin-1/2 fermions interacting with a spin-1/2 impurity. Thus, we study the scattering of fermionic quasiparticles (propagating along spin chains) by a pair of localized magnetic impurities. At low temperature, the localized spin-1/2 magnets are shielded by the chain "spins" via the Kondo effect. We calculate the Kondo temperature T (K) and derive the temperature dependence of the entropy, the specific heat and the "magnetic susceptibility" of the dot for T >> T (K). Our results can be generalized to the case of antiferromagnetic XX chains.