Phase diagram of the Kondo model on the zigzag ladder

The effect of next-nearest-neighbor hopping t(2) on the ground-state phase diagram of the one-dimensional Kondo lattice is studied with density-matrix renormalization-group techniques and by comparing with the phase diagram of the classical-spin variant of the same model. For a finite t(2), i.e., for a zigzag-ladder geometry, indirect antiferromagnetic interactions between the localized spins are geometrically frustrated. We demonstrate that t(2) at the same time triggers several magnetic phases which are absent in the model with nearest-neighbor hopping only. For strong J, we find a transition from antiferromagnetic to incommensurate magnetic short-range order, which can be understood entirely in the classical-spin picture. For weaker J, a spin-dimerized phase emerges, which spontaneously breaks the discrete translation symmetry. The phase is not accessible to perturbative means but is explained, on a qualitative level, by the classical-spin model as well. Spin dimerization alleviates magnetic frustration and is interpreted as a key to understand the emergence of quasi-long-range spiral magnetic order, which is found at weaker couplings. The phase diagram at weak J, with gapless quasi-long-range order on top of the twofold degenerate spin-dimerized ground state, competing with a nondegenerate phase with gapped spin (and charge) excitations, is unconventional and eludes an effective low-energy spin-only theory.