Fulsebakke, Jorgen
(2016)
Projections and correlations
in the fractional quantum Hall effect.
PhD thesis, National University of Ireland Maynooth.
Abstract
More than 30 years after its surprising experimental discovery, the quantum
Hall effect remains one of the most active and interesting fields of research
in condensed matter physics. The theory pertaining to the phenomenon comprises
a hugely varied and fascinating body of work, incorporating frameworks
such as variational trial wavefunctions, topological phases, conformal field theory
and more. There are reasons to expect that some phases of the system
harbour nonabelian excitations: particles whose interchange affects the state
of the whole system in a way depending on the order of exchange. This has
been proposed as a suitable basis for noise resistant quantum computing.
The excitations are an emergent property of the totality of the system,
whose main active constituent is the well understood electron. The electrons
act together in such a way as to manifest exotic quasiparticles; these kinds of
strong correlations are a general feature of the system. One can argue that the
quantum Hall effect shows the limits of reductionism.
In this work we focus on trial wavefunctions as descriptions of the phenomenon.
Although highly succesful in the past their evaluation is often impeded
by a feature known as lowest Landau level projection. We approach the
projection from several angles and in this context introduce an effective and
general technique termed energy projection. Using this we examine several
trial wavefunctions that have been difficult to deal with in the past.
The quantity known as the pair correlation function is an important tool
for the analysis of wavefunctions. Its study, however, has often been mainly
qualitative in the literature. We construct an expansion useful for exact characterisation
and comparison of pair correlations and show that it has desirable
properties as compared to a similar preexisting expansion. This is then used
to scale pair correlation functions to macroscopic sizes.
| Item Type: |
Thesis
(PhD)
|
| Keywords: |
Projections; correlations;
fractional quantum Hall effect; |
| Academic Unit: |
Faculty of Science and Engineering > Mathematical Physics |
| Item ID: |
7590 |
| Depositing User: |
IR eTheses
|
| Date Deposited: |
02 Nov 2016 11:59 |
| URI: |
|
| Use Licence: |
This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available
here |
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