Atkinson, Bill A

S. Johri and R. Bhatt developed a real-space renormalization group approach aimed at extracting the localized single-particle eigenstates of the Anderson model from a large system by identifying clusters of resonant site potentials. E. Campbell generalized this real-space renormalization group approach using standard perturbation theory. Both approaches were intended to approximate the single-particle density of states of the Anderson model. In this thesis, we aimed to test the potential of applying a similar real-space renormalization group approach to calculate the density of states of the interacting Anderson-Hubbard model. Our interest in the density of states of this model is due to a V-shaped zero-bias anomaly in two-dimensional systems. A real-space renormalization group approach is best applied to a one-dimensional system. We found that the zero-bias anomaly is not V-shaped in one-dimension. To test the potential of a real-space renormalization group approach, we used the cluster approach which is the same as the non-interacting renormalization group approach but without the perturbation theory and found that for strong disorder this technique could accurately calculate the density of states over a wide range of energies but deviated from exact results at the band edge, at $\omega=\pm U$ and near $\omega=0$. The first two inaccuracies will be reduced with a proper real-space renormalization group approach. We suspect that the last inaccuracy is associated with long range physics and may be difficult to recover. We also developed a technique that adjusts the identification of clusters in the cluster approach to improve the computation time of the density of states with minimal loss of accuracy in a tunable range around the Fermi level. We found that this technique significantly reduced the computation time and was able to preserve the density of states near the Fermi level, except at the smallest energies near $\omega=0$.

Author Keywords: Anderson-Hubbard model, renormalization group, Strong electron correlations, Zero-bias anomaly

Many of the most interesting electronic behaviours currently being studied are associated with strong correlations. In addition, many of these materials are disordered either intrinsically or due to doping. Solving interacting systems exactly is extremely computationally expensive, and approximate techniques developed for strongly correlated systems are not easily adapted to include disorder. As a non-interacting disordered model, it makes sense to consider the Anderson model as a first step in developing an approximate method of solution to the interacting and disordered Anderson-Hubbard model. Our renormalization group (RG) approach is modeled on that proposed by Johri and Bhatt [23]. We found an error in their work which we have corrected in our procedure. After testing the execution of the RG, we benchmarked the density of states and inverse participation ratio results against exact diagonalization. Our approach is significantly faster than exact diagonalization and is most accurate in the limit of strong disorder.

Author Keywords: disorder, localization, real-space renormalization, strong correlations

There is an increasing global need for grid scale electrical energy storage to handle the implementation of intermittent renewable energy sources. Adiabatic compressed air energy storage is an emerging technology with similar performance to pumped hydro except it has the issue of heat loss during the compression stage. Previously, it has been considered to use sensible heat storage materials to store the heat created by compression in a thermal energy storage unit until energy is required, and then transfer the heat back to the air. This research proposes to instead use phase change materials to store the heat of compression, as this will reduce entropy generation and maximize roundtrip exergy efficiency. Different configurations and placements of the phase change materials are considered and exergy analyses are presented. The thermodynamic equations are derived and optimal setup conditions including amount of latent heat and melting temperatures are calculated.

Author Keywords: Compressed Air Energy Storage, Energy Storage, Exergy, Phase Change Materials