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 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.

Grantor dc:publisher

Universidade Federal de Pernambuco

Year dc:date.issued

2016

Author dc:creator

• MORENO TARQUINO, Juan Nicolas

Advisor dc:contributor.advisor

• MACEDO, Antonio Murilo Santos

• Matéria condensada
• Transporte quântico
• Caos quântico

Statement dc:rights

• openAccess
• Attribution-NonCommercial-NoDerivs 3.0 Brazil

Licence dc:rights.uri

• http://creativecommons.org/licenses/by-nc-nd/3.0/br/

Language dc:language.iso

eng

Repository record dc:identifier.uri

https://repositorio.ufpe.br/handle/123456789/24737

OAI identifier oai:identifier

oai:repositorio.ufpe.br:123456789/24737