Details
| Original language | English |
|---|---|
| Qualification | Doctor rerum naturalium |
| Awarding Institution | |
| Supervised by |
|
| Date of Award | 12 Dec 2018 |
| Place of Publication | Hannover |
| Publication status | Published - 2 Jan 2019 |
Abstract
Keywords
- Bethe ansatz, anyons, WZNW models, anyon condensation
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Hannover, 2019. 114 p.
Research output: Thesis › Doctoral thesis
}
TY - BOOK
T1 - Non-Abelian quasi-particles in electronic systems
AU - Borcherding, Daniel
N1 - Doctoral thesis
PY - 2019/1/2
Y1 - 2019/1/2
N2 - Ever since the proposal of Kitaev for decoherence-free quantum computing based on non-Abelian anyons physical realizations of these exotic particles have been investigated extensively. Starting from one-dimensional models of interacting fermions with different symmetries the emergence and condensation of $\mathfrak{su}(2)_{N_f}$, $\mathfrak{su}(3)_{N_f}$ and $\mathfrak{so}(5)_{N_f}$ anyons is studied in the framework of integrable perturbed WZNW models. For sufficiently small temperatures and fields non-Abelian anyons residing on massive solitonic excitations are identified by their quantum dimension. By tuning the external fields the density of anyons can be increased continuously to study the effect of interactions between them. For each model the conformal field theories describing the various collective states of the interacting anyons are determined and a phase diagram for the anyonic modes is proposed.
AB - Ever since the proposal of Kitaev for decoherence-free quantum computing based on non-Abelian anyons physical realizations of these exotic particles have been investigated extensively. Starting from one-dimensional models of interacting fermions with different symmetries the emergence and condensation of $\mathfrak{su}(2)_{N_f}$, $\mathfrak{su}(3)_{N_f}$ and $\mathfrak{so}(5)_{N_f}$ anyons is studied in the framework of integrable perturbed WZNW models. For sufficiently small temperatures and fields non-Abelian anyons residing on massive solitonic excitations are identified by their quantum dimension. By tuning the external fields the density of anyons can be increased continuously to study the effect of interactions between them. For each model the conformal field theories describing the various collective states of the interacting anyons are determined and a phase diagram for the anyonic modes is proposed.
KW - Bethe ansatz
KW - anyons
KW - WZNW models
KW - anyon condensation
U2 - 10.15488/4280
DO - 10.15488/4280
M3 - Doctoral thesis
CY - Hannover
ER -