A Luttinger Liquid Coupled to a Quantum Spin Bath: Flow Equation Approach to the Kondo Necklace Model

We study a lattice realization of a Luttinger liquid interacting with a bath of quantum spins in terms of an antiferromagnetic S=1/2 Heisenberg chain, where each spin is also coupled to a \sigma=1/2 Kondo spin degree of freedom. This model describes the low-energy spin dynamics in quasi one dimensional materials, where the electronic spins of the magnetic ions interact with those of impurities, nuclei and possibly other spin species present in their environment. For large ferromagnetic and antiferromagnetic Kondo interaction J' there are two phases corresponding to an effective spin-1 Heisenberg chain and a dimerised spin-1/2 ladder, respectively. For weak Kondo interaction we establish that the Kondo interaction drives the system to a strong coupling regime. This suggests that J'=0 is the only critical point in the system.