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Acta Physica Polonica A

Heavy Quasiparticles in Yb Compounds: The Renormalized Band Approach

Gertrud Zwicknagl

Published Jun 6, 2014• 0 citations
Publisher

Abstract

Results for the magnetic-eld-induced changes of the heavy quasiparticles in YbRh2Si2 are presented.The bands are determined by means of the Renormalized Band method.The progressive de-renormalization of the quasiparticles in the magnetic eld, as well as the many-body enhancement of the Zeeman splitting are accounted for, using eld-dependent quasiparticle parameters deduced from Numerical Renormalization Group studies.

DOI
10.12693/aphyspola.126.286

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•Nov 14, 2012•1 citation
Results for the magnetic-eld-induced changes of the heavy quasiparticles in YbRh2Si2 are presented.The bands are determined by means of the Renormalized Band method.The progressive de-renormalization of the quasiparticles in the magnetic eld, as well as the many-body enhancement of the Zeeman splitting are accounted for, using eld-dependent quasiparticle parameters deduced from Numerical Renormalization Group studies.
In this paper a recently developed projector-based renormalization method (PRM) for many-particle Hamiltonians is applied to the periodic Anderson model with the aim to describe heavy-fermion behavior. In this method high-energetic excitation operators instead of high energetic states are eliminated. We arrive at an effective Hamiltonian for a quasifree system which consists of two noninteracting heavy-quasiparticle bands. The resulting renormalization equations for the parameters of the Hamiltonian are valid for large as well as small degeneracy ${\ensuremath{\nu}}_{f}$ of the angular momentum. An expansion in $1∕{\ensuremath{\nu}}_{f}$ is avoided. Within an additional approximation which adapts the idea of a fixed renormalized fff level ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}}_{f}$, we obtain coupled equations for ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\epsilon}}}_{f}$ and the averaged fff occupation ⟨nf⟩⟨{n}_{f}⟩⟨nf​⟩. These equations resemble to a certain extent those of the usual slave boson mean-field (SB) treatment. In particular, for large ${\ensuremath{\nu}}_{f}$ the results for the PRM and the SB approach agree perfectly whereas considerable differences are found for small ${\ensuremath{\nu}}_{f}$.
We extend the renormalized quasiparticle description of the symmetric Anderson model in a magnetic field HHH, developed in earlier work, to the nonsymmetric model. The renormalized parameters are deduced from the low energy numerical renormalization group (NRG) fixed point for arbitrary field values. We find quasiparticle resonance widths, ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\Delta}}}_{\ensuremath{\sigma}}(H)$, which depend in general on the spin $\ensuremath{\sigma}$ as well as HHH. The low temperature static properties can be expressed completely in terms of these parameters, which can also be used as inputs for a renormalized perturbation theory. We show that taking into account repeated quasiparticle scattering gives results for the longitudinal and transverse dynamic spin susceptibilities which are in very good agreement with those obtained from direct NRG calculations.
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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.
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Actinide- and Lanthanide based compounds are often considered as heavy Fermion (HF) systems. The essential ingredient for these systems is a localized d- or f-shell electron per lattice site which hybridizes with a non-interacting conduction band of p- or d-shell electrons. For temperatures below the so called coherence temperature Tc, the localized electrons stop to act like mag- netic scatterers known from the Kondo effect. There the conduction band electrons screen the local magnetic moments coherently. As a main effect the conduction electrons build a Fermi liquid (FL) of quasiparticles with strongly enhanced masses which exceed 10-1000 times the mass of the original electrons. These enhancements can be seen experimentally in an increased heat capacity coefficient and Pauli susceptibility. \nIn this work we employ the periodic Anderson model (PAM) to describe the paramagnetic phase of the heavy Fermion compounds. To solve the compli- cated many body problem the dynamical mean-field theory is adopted with the numerical renormalization group technique as impurity solver. \nWe find that for low conduction band fillings Tc decreases drastically, which is in accordance with the exhaustion effect predicted by Nozières [5]. Additionally we find, that the form of the free conduction band density of states is decisive to obtain a FL or a Mott insulating (MI) phase for strongly depleted conduction band fillings. \nFurthermore we investigate the PAM on a bipartite lattice, the coherence temperatures for each sublattice and especially the case of vanishing hybridiza- tion for one sublattice. In the latter case the system resembles a conduction band with only half the localized moment sites coupled to it. Our results show that it depends strongly on the chosen parameters if there is only one scale for the whole lattice or two distinct scales for each sublattice. Especially decoupling one sublattice leads to two separated scales. \nIn the last part the attention is focused on the two-impurity Anderson model and its solution via the DMFT method. We investigate the Anderson model and compare results to direct NRG calculations. Importantly, the two-impurity DMFT method can be easier extended to multi-impurity systems than the NRG on its own. This might lead to a method to efficiently examine multi- impurity systems.