Heisenberg necklace model in a magnetic field
Here, we study the low-energy sector of the Heisenberg necklace model. Using the field-theory methods, we estimate how the coupling of the electronic spins with the paramagnetic Kondo spins affects the overall spin dynamics and evaluate its dependence on a magnetic field. We are motivated by the experimental realizations of the spin-1/2 Heisenberg chains in SrCuO 2 and Sr 2 CuO 3 cuprates, which remain one-dimensional Luttinger liquids down to temperatures much lower than the in-chain exchange coupling J. We also consider the perturbation of the energy spectrum caused by the interaction γ with nuclear spins (I=3/2) present on the same sites. We find that the resulting necklace model has a characteristic energy scale, Λ~J 1/3 (γI) 2/3 , at which the coupling between (nuclear) spins of the necklace and the spins of the Heisenberg chain becomes strong. Furthermore, this energy scale is insensitive to a magnetic field B. For μB B>Λ we find two gapless bosonic modes that have different velocities, whose ratio at strong fields approaches a universal number, 2√+1.