Transition from integrable to chaotic domain in spectra of spin chains
In this thesis we present an approach, similar to random matrix ensembles, in order to study the integrable-chaotic transition in the Heisenberg spin model. We consider three ways to break the integrability: presence on an external field on a single spin, coupling of an external random field with ea...
| Main Author: | MORENO TARQUINO, Juan Nicolas |
|---|---|
| Other Authors: | MACEDO, Antonio Murilo Santos |
| Format: | masterThesis |
| Language: | eng |
| Published: |
Universidade Federal de Pernambuco
2018
|
| Subjects: | |
| Online Access: |
https://repositorio.ufpe.br/handle/123456789/24737 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: |
In this thesis we present an approach, similar to random matrix ensembles, in order to study the integrable-chaotic transition in the Heisenberg spin model. We consider three ways to break the integrability: presence on an external field on a single spin, coupling of an external random field with each spin in the chain and next nearest neighbor interaction between spins. We propose a transition described by a power law in the spectral density, i.e. S(k) ∝ 1/kα, where α = 2 for the integrable case and α = 1 for the chaotic case, with 1 < α < 2 for systems in the crossover regime. The transition is also described by the behavior of the "burstiness" B and the Kullback–Leibler divergence DLK(PW−D(s)|Pdata(s)), where PW−D(s) and Pdata(s) are the Wigner-Dyson and the system’s spacing distribution respectively. The B coefficient is associated to a sequence of events in the system. The Kullback–Leibler divergence provides information on how two distributions differ from each other. From analyzing the behavior of these three quantities, we obtain a universal description of integrable-chaotic transition in the spin chains. |
|---|