The subject of this thesis is the application of the Renormalised Perturbation Theory (RPT) to models of magnetic impurities embedded in a non-magnetic host metal. The theoretical description of such models is particularly challenging, for they present strong correlations that render the usual perturbation theory around the non-interacting limit inapplicable. The RPT addresses this di fficulty by incorporating the concept of a quasi-particle into a perturbative framework, and organising the expansion in terms of the quasi-particle parameters of the model rather than the bare parameters; it can thus be carried out regardless of the strength of the interactions. In the present work we present an introduction to the theory and discuss in detail the calculation of the renormalised self-energy expansions for the Anderson impurity model. To cope with the complexity of high-order calculations we develop and implement a computer algorithm to automatically compute the diagrammatic expansion in the renormalised theory to any order. As a demonstration of the usefulness of the theory, we use it to calculate the conductance of a single quantum dot, and of two quantum dots with an inter-dot coupling, to leading order in the quasi-particle interaction. To perform calculations in the renormalised theory it is essential that the values of the renormalised parameters describing the quasi-particles are known. Here we develop a general method for determining them entirely within the RPT framework, which relies on constructing renormalisation flow equations relating the renormalised parameters of two models whose bare parameters differ in infinitesimally. By determining the renormalised parameters for a model with bare parameters that render it amenable to ordinary perturbation theory, and solving the flow equations to relate them to the renormalised parameters of models with progressively stronger correlations, we succeed in deducing the renormalised parameters for models with strong correlations.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:679681 |
| Date | January 2015 |
| Creators | Pandis, Vasileios |
| Contributors | Hewson, Alex C. |
| Publisher | Imperial College London |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/10044/1/29160 |
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