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arXiv:1408.5226 · Physical Review B

Interplay of localized and itinerant behavior in the one-dimensional Kondo-Heisenberg model

Neng Xie, Yi‐feng Yang

Published May 11, 2015• 11 citations
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Abstract

We use the density matrix renormalization group method to study the interplay of the localized and itinerant behaviors in the one-dimensional Kondo-Heisenberg model. We find signatures of simultaneously localized and itinerant behaviors of the local spins and attribute this duality to their simultaneous entanglement within the spin chain and with conduction electrons due to incomplete hybridization. We propose a microscopic definition of the hybridization parameter that measures this ``partial'' itinerancy. Our results provide a microscopic support for the dual nature of $f$ electrons and the resulting two-fluid behavior widely observed in heavy electron materials.

DOI
10.1103/physrevb.91.195116

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We use the density matrix renormalization group method to study the interplay of the localized and itinerant behaviors in the one-dimensional Kondo-Heisenberg model. We find signatures of simultaneously localized and itinerant behaviors of the local spins and attribute this duality to their simultaneous entanglement within the spin chain and with conduction electrons due to incomplete hybridization. We propose a microscopic definition of the hybridization parameter that measures this ``partial'' itinerancy. Our results provide a microscopic support for the dual nature of fff electrons and the resulting two-fluid behavior widely observed in heavy electron materials.
We use the density matrix renormalization group method to study the properties of the one-dimensional Kondo-Heisenberg model doped with Kondo holes. We find that the perturbation of the Kondo holes to the local hybridization exhibits spatial oscillation pattern and its amplitude decays exponentially with distance away from the Kondo hole sites. The hybridization oscillation is correlated with both the charge density oscillation of the conduction electrons and the oscillation in the correlation function of the Heisenberg spins. In particular, we find that the oscillation wavelength for intermediate Kondo couplings is given by the Fermi wavevector of the large Fermi surface even before it is formed. This suggests that heavy electrons responsible for the oscillation are already present in this regime and start to accumulate around the to-be-formed large Fermi surface in the Brillouin zone.
Topological Kondo insulators are strongly correlated materials where itinerant electrons hybridize with localized spins, giving rise to a topologically nontrivial band structure. Here, we use nonperturbative bosonization and renormalization-group techniques to study theoretically a one-dimensional topological Kondo insulator, described as a Kondo-Heisenberg model, where the Heisenberg spin-1/2 chain is coupled to a Hubbard chain through a Kondo exchange interaction in the p-wave channel (i.e., a strongly correlated version of the prototypical Tamm-Schockley model). We derive and solve renormalization-group equations at two-loop order in the Kondo parameter, and find that, at half filling, the charge degrees of freedom in the Hubbard chain acquire a Mott gap, even in the case of a noninteracting conduction band (Hubbard parameter U=0). Furthermore, at low enough temperatures, the system maps onto a spin-1/2 ladder with local ferromagnetic interactions along the rungs, effectively locking the spin degrees of freedom into a spin-1 chain with frozen charge degrees of freedom. This structure behaves as a spin-1 Haldane chain, a prototypical interacting topological spin model, and features two magnetic spin-1/2 end states for chains with open boundary conditions. Our analysis allows us to derive an insightful connection between topological Kondo insulators in one spatial dimension and the well-known physics of the Haldane chain, showing that the ground state of the former is qualitatively different from the predictions of the naive mean-field theory.
We investigate interplay of topological and Kondo effects in a one-dimensional Kondo–Heisenberg model with nontrivial conduction band using the density matrix renormalization group method. By analyzing the density profile, the local hybridization, and the spin/charge gap, we find that the Kondo effect can be destructed at edges of the chain by the topological end state below a finite critical Kondo coupling <?CDATA JKc{J}_{{\rm{K}}}^{{\rm{c}}}JKc​?> J K c . We construct a phase diagram characterizing the transition of the end states.
A one-dimensional model Hamiltonian that is motivated by the recent discovery of the heavy-fermion behavior in the cuprates of the Nd2{\mathrm{Nd}}_{2}Nd2​CuO4{\mathrm{O}}_{4}O4​ type is studied. It consists of $t\ensuremath{-}J$ interacting conduction electrons coupled to a lattice of localized spins through a Kondo exchange term JK{J}_{K}JK​. Exact diagonalization and density-matrix renormalization-group methods are used. The latter method is generalized to arbitrary densities. At half filling, a spin gap opens for all JK>0{J}_{K}>0JK​>0. Away from half filling it is shown that, at strong JK{J}_{K}JK​, the ground state is an unsaturated ferromagnet. At weak JK{J}_{K}JK​ the system is in a paramagnetic phase with enhanced Ruderman-Kittel-Kasuya-Yosida (RKKY) correlations. The importance of self-screening of the local moments in the depletion regime is discussed. We argue that these findings transcend the specifics of the model.
We investigate the magnetic order and related strongly correlated effects in a one-dimensional Ising-Kondo lattice with transverse field. This model is the anisotropic limit of the conventional isotropic Kondo lattice model, in the sense that the itinerant electrons interact with the localized magnetic moments via only longitudinal Kondo exchange. Adopting the numerical density-matrix renormalization group method, we map out the ground-state phase diagram in various parameter spaces. Depending on the Kondo coupling and filling number, three distinct phases, including a metallic paramagnetic, a metallic ferromagnetic, and a gapped spin-density wave phase, are obtained. The spin-density wave is characterized by an ordering wave vector, which coincides with the nesting wave vector of the Fermi surface. This makes the corresponding magnetic transition a spin analog of the Peierls transition occurring in the one-dimensional metal. Moreover, by analyzing the momentum distribution function and charge correlation function, the conduction electrons are shown to behave like free spinless fermions in the ferromagnetic phase. We finally discuss the effect of the repulsive Hubbard interaction between conduction electrons. Our paper enriches the Kondo physics and deepens the current understanding of the heavy fermion compounds.
The paramagnetic metallic phase of the one-dimensional Kondo lattice model is studied by the density matrix renormalization group method. We observe charge and spin Friedel oscillations. They reflect the long- range charge-charge and spin-spin correlation functions. The observed oscillations are consistent with a Tomonaga-Luttinger liquid. From the period of the oscillations it is concluded that the Fermi surface is large, including both the conduction electrons and the localized spins, kF{\mathit{k}}_{\mathit{F}}kF​=\ensuremath{\pi}(1+nc{\mathit{n}}_{\mathit{c}}nc​)/2, where nc{\mathit{n}}_{\mathit{c}}nc​ is the density of conduction electrons. \textcopyright{} 1996 The American Physical Society.