Understanding how the various electronic properties of matter emerge from the motion and interaction of electrons has been an important goal of physics since the early 1900s. One important tool has been the study of quantum lattice models, which can be considered as simplified depictions of solids. Provided that the system is small enough, it is possible to solve the low energy spectrum accurately with numerical methods. Like most problems in modern physics, studying lattice models requires extensive numerical computation. Traditionally, computer programs have been written to run on the central processing unit, but in recent years, various new parallel computing coprocessors have been introduced. Graphics processing units, which were originally added to render images on the computer screen, can now also be used for general purpose computation. Another new platform is the Xeon Phi coprocessor, specifically designed to accelerate parallel programs. Both of these coprocessors are parallel systems, where there are hundreds or thousands of computational threads running concurrently. This poses challenges in designing and implementing algorithms that benefit from the parallelism. In this Thesis, we implement the exact diagonalization method on graphics processors and the Xeon Phi. We apply it on topological lattice models, which have been under intense study recently. They feature topological phases that cannot be explained with Landau's symmetry-breaking theory, but instead require studying the topological properties of the ground state. One key quantity in identifying the phases is the Chern number that is related to the transverse conductance in quantum Hall phases. In the so called checkerboard model, we show that the topological ground state can withstand strong local impurities. With increasing impurity density, we observe transitions to a metallic state and an insulating state. In another model, the Haldane-Hubbard model, we study the phase diagram with changing on-site interaction and sublattice potential. We find an interesting intermediate topological phase, where the symmetry of the up and down spins breaks spontaneously.
|Translated title of the contribution||Topologisten hilamallien ratkaisua laskentasuorittimilla|
|Publication status||Published - 2016|
|MoE publication type||G5 Doctoral dissertation (article)|
- lattice model
- Xeon Phi
- Lanczos algorithm