Numerical Investigation of Exotic Phases in Quantum Lattice Models.
PhD thesis, National University of Ireland Maynooth.
In this thesis we present details of the design, development and
application of a large scale exact diagonalisation code named
DoQO (Diagonalisation of Quantum Observables). Among the
features of this code are its ability to exploit physical symmetries
and the fact that it has been designed to run in parallel
to take advantage of modern high performance computing resources.
The primary motivation for developing this code has
been the investigation of exotic phases in quantum lattice models,
and in particular of topological phases. A signicant portion
of the thesis concerns the investigation of supersymmetric lattice
models, which involves signicant use of the developed DoQO
code. These are a relatively new (2003) family of models consisting
of spinless fermions hopping on a lattice with the interactions
tuned to a point where the spectrum exhibits supersymmetry.
These models are extremely rich in the physics that they exhibit.
Among the phases believed to exist in these models are critical,
super-frustrated and super-topological phases. DoQO was also
employed to investigate nite size eects in the Kitaev honeycomb
lattice model. This is a spin model which exhibits both
abelian and non abelian topological phases.
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