Magnetic frustration in itinerant systems: the Kondo polaron problem

We study the interplay between magnetic frustration and Kondo screening in Kondo lattices by analyzing the $J_1$-$J_2$ antiferromagnetic chain coupled to a conduction band. The system is tuned to the Majumdar-Ghosh point $J_2=J_1/2$ which stabilizes a dimer valence-bond solid at weak Kondo coupling $J_K$. We use an effective low-energy theory to demonstrate that sufficiently large $J_K$ results in a proliferation of ``Kondo polarons'', i.e. Kondo-screened domain-wall excitations of the dimer state, and collapse of the dimer order via a 2nd order quantum phase transition. At the quantum critical point, $J_K=J_K^c$, these polarons become gapless, and we argue that the transition itself belongs to a 2D Ising universality class. For $J_K>J_K^c$ increasing concentration of the polarons leads to a continuous growth of the electron Fermi momentum until all spins are absorbed by the Fermi sea.