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arXiv:2209.04231 · Physical review. B./Physical review. B

Competing states in the two-dimensional frustrated Kondo-necklace model

Matthias Peschke, Boris Ponsioen, Philippe Corboz

Published Nov 23, 2022• 6 citations
arXivHTMLPDF

Abstract

The interplay between Kondo screening, indirect magnetic interaction, and geometrical frustration is studied in the two-dimensional Kondo-necklace model on the triangular lattice. Using infinite projected entangled pair states (iPEPS), we compute the ground state as a function of the antiferromagnetic local Kondo interaction ${J}_{K}$ and the Ising-type direct spin-spin interaction ${I}_{z}$. As opposed to previous studies, we do not find partial Kondo screening (PKS) in the isotropic limit ${I}_{z}=0$ but the same behavior as in the unfrustrated case, i.e., a direct phase transition between the paradigmatic phases of the Doniach competition: (i) a disordered phase consisting of local spin singlets at strong ${J}_{K}$ and (ii) a magnetically ordered phase at weak ${J}_{K}$. For ${I}_{z}>0$, we find a PKS ground state but again oppositely to previous studies, we find that the PKS ground state is in strong competition with a second ground state candidate not found before. This state is characterized by a strongly polarized central spin in each hexagon and its antiparallel, weakly polarized (i.e., partially screened) neighbors. We name it the central spin phase.

DOI
10.1103/physrevb.106.205140

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The interplay between Kondo screening, indirect magnetic interaction, and geometrical frustration is studied in the two-dimensional Kondo-necklace model on the triangular lattice. Using infinite projected entangled pair states (iPEPS), we compute the ground state as a function of the antiferromagnetic local Kondo interaction JK{J}_{K}JK​ and the Ising-type direct spin-spin interaction Iz{I}_{z}Iz​. As opposed to previous studies, we do not find partial Kondo screening (PKS) in the isotropic limit Iz=0{I}_{z}=0Iz​=0 but the same behavior as in the unfrustrated case, i.e., a direct phase transition between the paradigmatic phases of the Doniach competition: (i) a disordered phase consisting of local spin singlets at strong JK{J}_{K}JK​ and (ii) a magnetically ordered phase at weak JK{J}_{K}JK​. For Iz>0{I}_{z}>0Iz​>0, we find a PKS ground state but again oppositely to previous studies, we find that the PKS ground state is in strong competition with a second ground state candidate not found before. This state is characterized by a strongly polarized central spin in each hexagon and its antiparallel, weakly polarized (i.e., partially screened) neighbors. We name it the central spin phase.
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The effect of next-nearest-neighbor hopping t2{t}_{2}t2​ 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 t2{t}_{2}t2​, i.e., for a zigzag-ladder geometry, indirect antiferromagnetic interactions between the localized spins are geometrically frustrated. We demonstrate that t2{t}_{2}t2​ at the same time triggers several magnetic phases which are absent in the model with nearest-neighbor hopping only. For strong JJJ, we find a transition from antiferromagnetic to incommensurate magnetic short-range order, which can be understood entirely in the classical-spin picture. For weaker JJJ, 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 JJJ, 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.
In this work the ordering processes in classical frustrated Ising models and the ground-state behavior of frustrated quantum spin models are investigated. In the first part the phase transition from a high-temperature paramagnetic phase to a antiferromagnetic ground state is analyzed for the square-lattice Ising model with competing antiferromagnetic interactions between nearest- and next-nearest-neighbor spins. In the case of spatially isotropic interactions the phase transition to a collinear state is of special interest. Using Monte-Carlo simulations on finite lattices as well as field-theoretical methods for the continuous model it is shown that depending on the frustration three different sectors can be distinguished that show (i) Ising-universal behavior (ii) Ashkin-Teller-like non-universal behavior (varying critical exponents) and (iii) non-critical first-order behavior. For spatially anisotropic interactions the emergence of an intermediate incommensurate phase is verified by means of Monte-Carlo simulations which has been predicted by earlier mean-field calculations. The nature of this phase is studied analyzing spin-spin correlation functions and its ordering wave-vector reveals a strong temperature and size dependence. In the second part the influence of quantum fluctuations on classical antiferromagnetic ground states are investigated in anisotropic quantum spin-1/2 Heisenberg models with competing interactions. Using quantum Monte-Carlo simulations, exact diagonalization and perturbation theory the ground-state phase diagrams are calculated for a square lattice with nearest- and next-nearest-neighbor interactions and a honeycomb lattice with up to third-nearest-neighbor interactions whereby the fluctuations are chosen to be non-frustrating. For both cases the stability regions of classical magnetic states are identified and an intermediate phase is detected that shows no sign of long-range magnetic order. Further calculations also rule out valence-bond-crystal or topological order for this state, thus a quantum disordered ground state is stabilized in these models.
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