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 investigate the dynamical properties of the one-dimensional Hubbard model using the quantum Monte Carlo method and the numerical analytic continuation method based on the maximum entropy principle. Results for the spin, charge and current excitation spectrum are presented for various values of the coupling and the band filling for the system of 24 sites with the periodic boundary condition. We find that the total spectral density of the spin excitation exhibits a gapless structure irrespective of the coupling or the band filling. The charge excitation spectrum, on the other hand, clearly shows the gap formation at the half filled band and shifts its weight toward the higher energy region with increase of the coupling. This charge excitation gap, however, disappears with the hole doping. We also discuss the momentum dependence of the spectral functions.
We present, in this dissertation, a numerical simulation method to study interacting fermion systems. The general simulation procedures are discussed in connection with a description of a Quantum Monte Carlo simulation algorithm for interacting electrons on lattices. The algorithm presented here has been used to simulate interacting electrons on lattices, and it makes possible the study of substantially larger systems than can be studied by other numerical methods. As long as certain limits of applicability are respected, model Hamiltonians of interacting electrons can be studied without resort to uncontrolled approximations. The method then provides nearly exact solutions to model Hamiltonians of many-body systems, in the sense that the degree of error can be controlled. We also discuss some results obtained from simulations of the extended Hubbard model and and the periodic Anderson model. For the extended Hubbard model in two dimensions, different regions are identified where electron correlation produces antiferromagnetism, charge-density-waves, and singlet pairing superconducting behaviors. We also find regions where transitions from one type of correlation to another occur. For the symmetric periodic Anderson model, we observe the formation of local spin moments at high temperatures and their quenching at low temperatures, as in the single impurity Anderson model. In addition, we find antiferromagnetic interaction between f local moments at low temperatures which are not present in a single impurity problem.
We investigate the effect of the Coulomb interaction,
Ucf, between the conduction and
f electrons in the periodic Anderson model using the density matrix renormalization group algorithm. We calculate the excitation spectrum of the half-filled symmetric model with an emphasis on the spin and charge excitations. In the one-dimensional version of the model, it is found that the spin gap is smaller than the charge gap below a certain value of
Ucf and the reversed inequality is valid for stronger
Ucf. This behavior is also verified by the behavior of the spin and density correlation functions. We also perform a quantum information analysis of the model and determine the entanglement map of the
f and conduction electrons. It is revealed that for a certain
Ucf the ground state is dominated by the configuration in which the conduction and
f electrons are strongly entangled, and the ground state is almost a product state. For larger
Ucf, the sites are occupied alternatingly dominantly by two
f electrons or by two conduction electrons.
The dynamic spin and charge correlation functions are computed for the one-dimensional t-J model with use of world-line quantum Monte Carlo and the maximum-entropy method. By comparing our results with exactly known limits, we are able to discern the power and limitations of this method. The spin excitation spectrum shows gapless spin excitations for q=2
kF when J\ensuremath{\le}2t and for q=\ensuremath{\pi} when J>3.25t where phase separation occurs. Also, intermediate values of J/t show no spin gap for the large electron filling (${\mathrm{\ensuremath{\rho}}}_{0}$=0.75) considered here. For J\ensuremath{\le}2t, the charge correlations are dominated at high frequencies by excitations which are related to the particle-hole excitations found for J=0, but a low-frequency mode appears at finite values of J, which is likely related to the binding of electron pairs.