Brennan, John
(2018)
The Kitaev Model on Surfaces
with Lattice Defects and of
Higher Genus.
PhD thesis, National University of Ireland Maynooth.
Abstract
The quantum phase of a physical system is defined as its ground state. As
examples of quantum phases we mention super
uids, superconductors, Bose-
Einstein condensates and quantum Hall states. Different phases of a system
originate from the different ways a systems' constituents can be organised or, in
other words, the different orders of the system. Landau had the insight that the
difference between two phases can be attributed to the corresponding orders
having different symmetries [1]. Also, the transition between phases can be
associated with the breaking of symmetries. This insight led to Ginzburg and
Landau describing orders using local order parameters and developing a general
theory of phase transitions based on symmetry breaking. This theory was
successful in describing a large number of observed phases of matter. However,
phases of matter have been discovered which cannot be described using a
local order parameter and Landau's theory of symmetry breaking known as
topological phases.
| Item Type: |
Thesis
(PhD)
|
| Keywords: |
The Kitaev Model; Surfaces; Lattice Defects; Higher Genus; |
| Academic Unit: |
Faculty of Science and Engineering > Mathematical Physics |
| Item ID: |
10252 |
| Depositing User: |
IR eTheses
|
| Date Deposited: |
28 Nov 2018 14:47 |
| 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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