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Register a new userCoherence Temperature in the Diluted Periodic Anderson Model
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Added by
Natanael De Carvalho Costa
Publication date
2018
fields
Physics
and research's language is
English
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The Kondo and Periodic Anderson Model (PAM) are known to provide a microscopic picture of many of the fundamental properties of heavy fermion materials and, more generally, a variety of strong correlation phenomena in $4f$ and $5f$ systems. In this paper, we apply the Determinant Quantum Monte Carlo (DQMC) method to include disorder in the PAM, specifically the removal of a fraction $x$ of the localized orbitals. We determine the evolution of the coherence temperature $T^*$, where the local moments and conduction electrons become entwined in a heavy fermion fluid, with $x$ and with the hybridization $V$ between localized and conduction orbitals. We recover several of the principal observed trends in $T^*$ of doped heavy fermions, and also show that, within this theoretical framework, the calculated Nuclear Magnetic Resonance (NMR) relaxation rate tracks the experimentally measured behavior in pure and doped CeCoIn$_5$. Our results contribute to important issues in the interpretation of local probes of disordered, strongly correlated systems.
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Recently, dynamical mean field theory calculations have shown that kinks emerge in the real part of the self energy of strongly correlated metals close to the Fermi level. This gives rise to a similar behavior in the quasi-particle dispersion relation as well as in the electronic specific heat. Since f-electron systems are even more strongly correlated than the -hitherto studied- d-electron systems we apply the dynamical mean field approach with the numerical renormalization group method as impurity solver to study whether there are kinks in the periodic Anderson model.
A basis of Bloch waves, distorted locally by the random potential, is introduced for electrons in the Anderson model. Matrix elements of the Hamiltonian between these distorted waves are averages over infinite numbers of independent site-energies, and so take definite values rather than distributions of values. The transformed Hamiltonian is ordered, and may be interpreted as an itinerant electron interacting with a spin on each site. In this new basis, the distinction between extended and localized states is clear, and edges of the bands of extended states, the mobility edges, are calculated as a function of disorder. In two dimensions these edges have been found in both analytic and numerical applications of tridiagonalization, but they have not been found in analytic approaches based on perturbation theory, or the single-parameter scaling hypothesis; nor have they been detected in numerical approaches based on scaling or critical distributions of level spacing. In both two and three dimensions the mobility edges in this work are found to separate with increasing disorder for all disorders, in contrast with the results of calculation using numerical scaling for three dimensions. The analytic trajectories are compared with recent results of numerical tridiagonalization on samples of over 10^9 sites. This representation of the Anderson model as an ordered interacting system implies that in addition to transitions at mobility edges, the Anderson model contains weaker transitions characterized by critical disorders where the band of extended states decouples from individual sites; and that singularities in the distribution of site energies, rather than its second moment, determine localization properties of the Anderson model.
The thermodynamic and transport properties of intermetallic compounds with Ce, Eu, and Yb ions are discussed using the periodic Anderson model with an infinite correlation between $f$ electrons. The slave boson solution of the periodic model shows that the Fermi liquid scale T$_0$ and the Kondo scale T$_K$ depend on the shape of the conduction electrons density of states ($c$ DOS) in the vicinity of the chemical potential, that the details of the band structure determine the ratio T$_0$/T$_K$, and that the crossover between the high- and low-temperature regimes in ordered compounds is system-dependent. A sharp peak in the $c$ DOS yields T$_0 ll$T$_K$ and explains the slow crossover observed in YbAl$_3$ or YbMgCu$_4$. A minimum in the $c$ DOS yields T$_0 gg$T$_K$, which leads to the abrupt transition between the high- and low-temperature regimes in YbInCu$_4$. In the case of CeCu$_2$Ge$_2$ and CeCu$_2$Si$_2$, where T$_0 simeq T_K$, the slave boson solution explains the pressure experiments which reveal sharp peaks in the T$^2$ coefficient of the electrical resistance, $A=rho(T)/T^2$, and the residual resistance. These peaks are due to the change in the degeneracy of the $f$ states induced by the applied pressure. We show that the low-temperature response of the periodic Anderson model can be enhanced (or reduced) with respect to the predictions based on the single-impurity models that give the same high-temperature behavior.
Motivated by recent photoemission and pump-probe experiments, we report determinant Quantum Monte Carlo simulations of hybridization fluctuations in the half-filled periodic Anderson model. A tentative phase diagram is constructed based solely on hybridization fluctuation spectra and reveals a crossover regime between an unhybridized selective Mott state and a fully hybridized Kondo insulating state. This intermediate phase exhibits nonlocal hybridization fluctuations and consequentially the so-called band bending and a direct hybridization gap as observed in angle-resolved photoemission spectroscopy and optical conductivity. This connects the band bending with the nonlocal hybridization fluctuations as proposed in latest ultrafast optical pump-probe experiment. The Kondo insulating state is only established at lower temperatures with the development of sufficiently strong inter-site hybridization correlations. Our work suggests a unified picture for interpreting recent photoemission, pump-probe, and optical observations and provides numerical evidences for the importance of hybridization fluctuations in heavy fermion physics.
We report a Determinant Quantum Monte Carlo investigation which quantifies the behavior of the susceptibility and the entropy in the framework of the periodic Anderson model (PAM), focussing on the evolution with different degree of conduction electron (c) -local moment (f) hybridization. These results capture the behavior observed in several experiments, including the universal behavior of the NMR Knight shift anomaly below the crossover temperature, $T^{ast}$. We find that $T^{ast}$ is a measure of the onset of c-f correlations and grows with increasing hybridization. These results suggest that the NMR Knight shift and spin-lattice relaxation rate measurements in non-Fermi liquid materials are strongly influenced by temperature-dependent hybridization processes. Our results provide a microscopic basis for the phenomenological two-fluid model of Kondo lattice behavior, and its evolution with pressure and temperature.
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