Magnetic susceptibility of a periodic Anderson model defined in infinite dimensions is investigated using the quantum Monte Carlo method. Special attention is paid to the enhancement of the interband contribution to the susceptibility (the Van Vleck term). It is found that the interband contribution is enhanced by the electron-electron interaction, but the enhancement is weaker than the dynamical mass enhancement. In particular, when the mixing between conduction electrons and f -electrons is small compared to the bandwidth, the enhancement of the interband contribution becomes much smaller than the dynamical mass enhancement as the interaction becomes strong.
Magnetic susceptibility of a periodic Anderson model defined in infinite dimensions is investigated using the quantum Monte Carlo method. Special attention is paid to the enhancement of the interband contribution to the susceptibility (the Van Vleck term). It is found that the interband contribution is enhanced by the electron-electron interaction, but the enhancement is weaker than the dynamical mass enhancement. In particular, when the mixing between conduction electrons and f -electrons is small compared to the bandwidth, the enhancement of the interband contribution becomes much smaller than the dynamical mass enhancement as the interaction becomes strong.
We investigate the inter-play of f-electron band dispersion and inter-f electron interactions on the gap in the one electron density of states (DOS) of the periodic Anderson model. The calculations are based on dynamical mean field theory and the numerical renormalization group method for the model in infinite dimensions. The local f-electron DOS at low energies for the electron-hole symmetric model with interactions is found to have a complete-gap, a pseudo-gap or to be gap-less, whenever these structures occur for the non-interacting model but the parameters that characterize these features are strongly renormalized. As the degree of f-electron dispersion is increased, when there is a complete gap, the many-body renormalization remains almost constant, but in the pseudo-gap case the renormalization increases. We calculate the sizes of gaps both in the local DOS and in the dynamic local susceptibilities. When the gap width is defined by the edges in the spectrum for the complete-gap model, the widths of the indirect gap and the spin gap are equal, independent of the degree of electron correlation. However, if the width is defined as the excitation energy between the peaks in the spectrum, then the ratio of the indirect gap to the spin gap increases and eventually saturates as the correlation increases. The value of this ratio depends on the f-electron band dispersion. We have also investigated the dependence of the shape of the interacting DOS on the f-band filling for different forms of f-band dispersion. When the f-band dispersion is small, the gap structure in the symmetric model vanishes as the filling factor decreases. When the model, including the dispersion, has no gap structure, the filling dependence on the DOS in low energies is similar to that for a single impurity Anderson model. The energy dispersion of the quasi-particle in the range, ε f < ε < ε f + U , is approximately explained by the renormalized band model in the cases of both large and small f-band dispersion.
We have studied the one-dimensional periodic, symmetric Anderson model at half filling in the presence of disorder using finite-temperature quantum Monte Carlo techniques. We have examined for the first time the disorder both in hybridization between the local f-orbitals and the conduction electrons and in the local f-site energy, using a uniform distribution of width . The f-orbital local magnetic moment, the uniform magnetic susceptibility, the charge compressibility, and the nearest-neighbour magnetic correlation function have been calculated as a function of the disorder distribution width . We find that the disorder in hybridization has a dramatic effect on the low-temperature magnetic properties exhibiting a non-Fermi-liquid behaviour, and that for the range of temperature studied the magnetic susceptibility can be scaled by a power law with an exponent that is in agreement with recent experiments. On the other hand, disorder in the local f-orbital energy level does not show a nonFermi liquid behaviour.
The Kondo and periodic Anderson models describe many of the qualitative features of local moments coupled to a conduction band, and thereby the physics of materials such as the heavy fermions. In particular, when the exchange coupling J or hybridization V between the moments and the electrons of the metallic band is large, singlets form, quenching the magnetism. In the opposite, small J or V, limit, the moments survive and the conduction electrons mediate an effective interaction which can trigger long-range, often antiferromagnetic order. In the case of the Kondo model, where the moments are described by local spins, Nozi\`eres considered the possibility that the available conduction electrons within the Kondo temperature of the Fermi surface would be insufficient in number to accomplish the screening. Much effort in the literature has been devoted to the study of the temperature scales in the resulting ``exhaustion'' problem and how the ``coherence temperature'' where a heavy Fermi liquid forms is related to the Kondo temperature. In this paper, we study a version of the periodic Anderson model in which some of the conduction electrons are removed in a way which avoids the fermion sign problem and hence allows low-temperature quantum Monte Carlo simulations which can access both singlet formation and magnetic ordering temperature scales. We are then able to focus on a somewhat different aspect of exhaustion physics than previously considered: the effect of dilution on the critical V for the singlet-antiferromagnetic transition.
We present a detailed, quantitative study of the competition between interaction- and disorder-induced effects in electronic systems. For this the Hubbard model with diagonal disorder (Anderson-Hubbard model) is investigated analytically and numerically in the limit of infinite spatial dimensions, i.e., within a dynamical mean-field theory, at half-filling. Numerical results are obtained for three different disorder distributions by employing quantum Monte Carlo techniques, which provide an explicit finite-temperature solution of the model in this limit. The magnetic phase diagram is constructed from the zeros of the inverse averaged staggered susceptibility. We find that at low enough temperatures and sufficiently strong interaction there always exists a phase with antiferromagnetic long-range order. A strong coupling anomaly, i.e., an increase of the N\'eel temperature for increasing disorder, is discovered. An explicit explanation is given, which shows that in the case of diagonal disorder this is a generic effect. The existence of metal-insulator transitions is studied by evaluating the averaged compressibility both in the paramagnetic and antiferromagnetic phases. A rich transition scenario, involving metal-insulator and magnetic transitions, is found and its dependence on the choice of the disorder distribution is discussed.
We report measurements of the spin susceptibility in dilute (rs up to $\ensuremath{\approx}10$) AlAs two-dimensional (2D) electrons occupying a single conduction-band valley with an anisotropic in-plane Fermi contour, characterized by longitudinal and transverse effective masses ml and mt. As the density is decreased, the spin susceptibility is significantly enhanced over its band value, reflecting the role of interaction. Yet the enhancement is suppressed compared to the results of quantum Monte Carlo based calculations that take the finite thickness of the electron layer into account but assume an isotropic effective mass equal to ml.mt. Proper treatment of an interacting 2D system with an anisotropic effective mass therefore remains a theoretical challenge.
We study dymanical properties of the symmetric periodic Anderson model in infinite dimensions by applying the quantum Monte Carlo method and the maximum entropy method. It is found that at low temperatures a gap is developed in the density of states, in the local spin excitation spectrum and in the local charge excitation spectrum. We clarify the effects of the strong electron correlation on structure of these dynamical quantities. As the strength of interaction increases, a sharp peak evolves at a low frequency region in the spin excitation spectrum while a broad shoulder appears at a higher frequency. On the other hand, as the interaction gets strong, the charge excitation spectrum splits into a low-frequency part and a high-frequency part; the low frequency part is severely suppressed by the interaction. The reliability and the limitation of the maximum entropy method are also discussed in detail.