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arXiv:0811.3000 · Physical Review B

Quasiparticles in the Kondo lattice model at partial fillings of the conduction band using the density matrix renormalization group

Sebastian Smerat, Ulrich Schollwöck, Ian P. McCulloch, Herbert Schoeller

Published Jun 4, 2009• 24 citations
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Abstract

We study the spectral properties of the one-dimensional Kondo lattice model as a function of the exchange coupling, the band filling, and the quasimomentum in the ferromagnetic and paramagnetic phases. Using the density-matrix renormalization group method, we compute the dispersion relation of the quasiparticles, their lifetimes, and the $Z$ factor. Sigrist et al. [Phys. Rev. Lett. 67, 2211 (1991)] provided the exact ground state and the quasiparticle-dispersion relation of the Kondo lattice model with one conduction electron. The quasiparticle could be identified as the spin polaron. Our calculations of the dispersion relation for partial band fillings give a result similar to the one-electron case, which suggests that the quasiparticle in both cases is the spin polaron. We find that the quasiparticle lifetime differs by orders of magnitude between the ferromagnetic and paramagnetic phases and depends strongly on the quasimomentum.

DOI
10.1103/physrevb.79.235107

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Publisher's Note: Quasiparticles in the Kondo lattice model at partial fillings of the conduction band using the density matrix renormalization group [Phys. Rev. B79, 235107 (2009)]

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We study the spectral properties of the one-dimensional Kondo lattice model as a function of the exchange coupling, the band filling, and the quasimomentum in the ferromagnetic and paramagnetic phases. Using the density-matrix renormalization group method, we compute the dispersion relation of the quasiparticles, their lifetimes, and the ZZZ factor. Sigrist et al. [Phys. Rev. Lett. 67, 2211 (1991)] provided the exact ground state and the quasiparticle-dispersion relation of the Kondo lattice model with one conduction electron. The quasiparticle could be identified as the spin polaron. Our calculations of the dispersion relation for partial band fillings give a result similar to the one-electron case, which suggests that the quasiparticle in both cases is the spin polaron. We find that the quasiparticle lifetime differs by orders of magnitude between the ferromagnetic and paramagnetic phases and depends strongly on the quasimomentum.
We compute the magnetic structure factor, the singlet correlation function, and the momentum distribution of the one-dimensional Kondo lattice model at the density \ensuremath{\rho}=0.7. The density-matrix--renormalization-group method is used. We show that in the weak-coupling regime, the ground state is paramagnetic. We argue that a Luttinger-liquid description of the model in this region is consistent with our calculations. In the strong-coupling regime, the ground state becomes ferromagnetic. The conduction electrons show a spinless-fermionlik
The first topic of this thesis is the study of many-body effects in an one-dimensional strongly correlated electronic system - the Kondo lattice model. This system is tackled numerically by means of the density matrix renormalization group, since analytic method, i.e., perturbation the- ory fail due to competing coupling constants. The Kondo lattice model consists of a conduction band of electrons which couple via a spin exchange coupling to a localized spin lattice. We study the spectral properties of the one-dimensional Kondo lattice model as a function of the exchange coupling, the band filling, and the quasimomentum in the ferromagnetic and paramagnetic phases. We compute the dispersion relation of the quasiparticles, their lifetimes, and the Z factor. The exact ground state and the quasiparticle-dispersion relation of the Kondo lattice model with one conduction electron are well known. The quasiparticle could be identified as the spin polaron. Our calculations of the dispersion relation for partial band fillings give a result similar to the one-electron case, which suggests that the quasiparticle in both cases is the spin polaron. We find that the quasiparticle lifetime differs by orders of magnitude between the ferromagnetic and paramagnetic phases and depends strongly on the quasimomentum. Further- more, we study the effects of the Coulomb interaction on the phase diagram, the static magnetic susceptibility and electron spin relaxation. We show that onsite Coulomb interaction supports ferromagnetic order and nearest neighbor Coulomb interaction drives, depending on the elec- tron filling, either a paramagnetic or ferromagnetic order. Furthermore, we calculate electron quasiparticle life times, which can be related to electron spin relaxation and decoherence times, and explain their dependence on the strength of interactions and the electron filling in order to find the sweet spot of parameters where the relaxation time is maximized. We find that effective exchange processes between the electrons dominate the spin relaxation and decoherence rate. In the second topic of this thesis, we numerically calculate the electron transport through carbon nanotube based quantum dot devices. We use a master equation’s approach in first order of the tunneling rate to the leads and an extended constant interaction model to model the carbon nanotube system. This work has been done in collaboration with two experimental groups and we compare their respective experimentally obtained data to our numerical calculations. In both collaborations striking similarity between the numerical data and the experimental data is found. In the first collaboration transport through a carbon nanotube peapod, i.e, a carbon nanotube filled with fullerenes, has been measured. We identify a small hybridization between a fullerene molecule and the surrounding carbon nanotube to be of crucial importance for the understanding of the transport data. In the second collaboration, electron transport through a carbon nanotube rope, i.e., a bundle of carbon nanotubes has been measured. Also here, hybridization between the different nanotubes plays a crucial role. Furthermore, an external magnetic field is applied, which enables the identification of specific spin states of the compound quantum dot system. This might be important for future applications of such devices in spin-dependent electronics.
Even though realistic one-dimensional experiments in the field of half-metallic semiconductors are not at hand yet, we are interested in the underlying fundamental physics. In this regard we study a one-dimensional ferromagnetic Kondo lattice model, a model in which a conduction band is coupled ferromagnetically to a background of localized d moments with coupling constant J(H), and investigate the T = 0 phase diagram as a function of the antiferromagnetic interaction J between the localized moments and the band-filling n, since it has been observed that doping of the compounds has led to formation of magnetic domains. We explore the spin-polaron formation by looking at the nearest-neighbour correlation functions in the spin and charge regimes for which we use the density matrix renormalization group method, which is a highly efficient method to investigate quasi-one-dimensional strongly correlated systems.
We consider a one-dimensional Hund lattice model where a conducting band is coupled with localized spins s = 1/2 interacting antiferromagnetically, with coupling constant J , and investigate the ground state phase diagram as a function of both the exchange coupling J and the band filling, n . From spin structure factor measurements we found different evolving magnetic orderings in the ground state related to the particle distribution in the systems, although no charge density waves are formed, as found from density-density correlation function measurements. We study the quasiparticle formation and phase separation using the density-matrix renormalization group method, which is a highly efficient method to investigate quasi-one-dimensional strongly correlated systems.
Thermodynamic properties of the one-dimensional Kondo lattice model at half-filling are studied by the density matrix renormalization group method applied to the quantum transfer matrix. Spin susceptibility, charge susceptibility, and specific heat are calculated down to T=0.1t for various exchange constants. The obtained results clearly show crossover behavior from the high temperature regime of nearly independent localized spins and conduction electrons to the low temperature regime where the two degrees of freedom couple strongly. The low temperature energy scales of the charge and spin susceptibilities are determined and shown to be equal to the quasiparticle gap and the spin gap, respectively, for weak exchange couplings.