Millar, Darragh
(2021)
Interacting Anyons in One and Two
Dimensions: Strong Zero Modes in
Anyon Chains and Non-Abelian
Anyons on a Torus.
PhD thesis, National University of Ireland, Maynooth.
Abstract
The work in this thesis is split into two distinct parts. The first focuses on
the identification and construction of strong zero modes in non-abelian anyon
chains. We show a Tambara-Yamagami chain is equivalent to a Zn chiral
clock model. We then present numerical evidence for a strong zero mode in
an SU(2)4 anyon chain. By rewriting the chain as an XXZ spin chain, we
construct the zero mode explicitly in terms of spin operators. Finally, we
write the zero mode in the diagrammatic formalism of anyons.
In the second part, we construct a hopping model of non-abelian anyons
on a torus. We demonstrate that that the model possesses a translational
symmetry around each non-trivial torus loop. By calculating the level spacing
statistics of the model, we show that the model is non-integrable for Fibonacci
anyons, Ising anyons and abelian anyons. Lastly, we carry out the groundwork
for a future project. We add local interactions between the anyons to the
Hamiltonian. We then calculate the entanglement spectrum of a ground state
of the system after cutting the torus into two cylindrical pieces. The low lying
states of this spectrum have a linear dispersion relation for several systems we
examined, suggesting the entanglement spectrum is described by a conformal
field theory spectrum.
| Item Type: |
Thesis
(PhD)
|
| Keywords: |
Interacting Anyons; One and Two
Dimensions; Strong Zero Modes; Anyon Chains; Non-Abelian
Anyons; Torus; |
| Academic Unit: |
Faculty of Science and Engineering > Theoretical Physics |
| Item ID: |
14865 |
| Depositing User: |
IR eTheses
|
| Date Deposited: |
29 Sep 2021 15:26 |
| 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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