Thermal and charge transport in correlated electron systems

In this thesis we investigate two topics. First, in chapter 2 we study the basis dependence of dynamical mean field theory. For the purpose of using this theory as a numerical tool for predicting properties of materials, the choice of a suitably localized basis is important. We propose and test a criterion for making this choice of basis. In the rest of the thesis we study thermal and charge transport in systems in which correlation effects are important. In chapter 3 we clarify some aspects in the calculation of the thermal transport coefficients. For a tight-binding Hamiltonian we discuss the approximate nature of the charge and the thermal current obtained by Peierls substitution. Using equation of motion we derive the thermal current for a generalized Hubbard model with density interaction. We identify a part which is the contribution to the thermal current from the long-range interactions. For the Hubbard model we derive expressions for the transport coefficients which are exact in the limit of large dimensions. In chapter 4 we study the form of the charge current operator in a down-folding scheme. By treating the down-folding procedure to lowest order in perturbation we derive expressions for the charge current in the low-energy sector. In chapter 5 we study the thermoelectric behavior of a heavy-fermion compound when it is close to an antiferromagnetic quantum critical point. When the low-energy spin fluctuations are quasi two-dimensional with a three-dimensional Fermi surface, the "hot" regions on the Fermi surface have a finite area. We argue that there is an intermediate energy scale where the qualitative aspects of the renormalized hot electrons are captured by a weak-coupling perturbative calculation. Due to enhanced scattering with the nearly critical spin fluctuations, the quasiparticle mass in the hot region is strongly renormalized. This accounts for the anomalous logarithmic temperature dependence of specific heat observed in these materials. We show that the same mechanism produces logarithmic temperature dependence in thermopower. This has been observed in CeCu6-xAux. We expect to see the same behavior from future experiments on YbRh2Si 2.