• JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
  • JoomlaWorks Simple Image Rotator
 
  Bookmark and Share
 
 
Doctoral Thesis
DOI
https://doi.org/10.11606/T.43.2019.tde-30102019-232405
Document
Author
Full name
Juan Pablo Ibieta Jimenez
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2019
Supervisor
Committee
Teotonio Sobrinho, Paulo (President)
Alcaraz, Francisco Castilho
Landi, Gabriel Teixeira
Miranda, Eduardo
Sá, Eduardo Peres Novais de
Title in Portuguese
Entropia topológica de emaranhamento em teorias de Higher Gauge Abelianas
Keywords in Portuguese
Entropia de Emaranhamento
Ordem Topológica
Teorias de Gauge
Abstract in Portuguese
Nós calculamos a entropia de emaranhamento topológica para um grande conjunto de modelos em dimensão d. Sabe-se que muitos sistemas quânticos podem ser construídos a partir de teorias de gauge na rede. Em dimensões maiores a 2 existem generalizações além das teorias de gauge. Chamadas higher gauge theories, estas são baseadas em generalizações de ordem superior do conceito de grupo. O nosso objeto de estudo é um conjunto grande de modelos d-dimensionais, que são obtidos a partir de teorias Abelianas de higher gauge. Neste trabalho, calculamos a entropia de emaranhamento para dito conjunto de modelos. O nosso formalismo permite fazer a maior parte do cálculo para dimensão arbitrária d. Mostramos que a entropia de emaran- hamento S_A , em uma sub-região A do sistema, é proporcional à log(GSD_Ã ), onde GSD_Ã é a degenerescência do estado fundamental de uma restrição particular do modelo na região A. Quando A tem a topologia de uma bola de dimensão d, a quantidade GSD_Ã conta o número de estados de borda. Neste caso, S_A escala com a área da borda (d 1)-dimensional de A. O resultado exato da entropia que obtemos está em concordância com os resultados conhecidos na literatura.
Title in English
Topological Entanglement Entropy in Abelian Higher Gauge Theories
Keywords in English
Entanglement Entropy
Gauge theories
Topological Order
Abstract in English
We compute topological entanglement entropy for a large set of lattice models in d-dimensions. It is well known that many such quantum systems can be constructed out of lattice gauge models. For dimensionality higher than 2 there are generalizations going beyond gauge theories. They are called higher gauge theories and rely on higher-order generalizations of groups. Our main concern is a large class of d-dimensional quantum systems derived from Abelian higher gauge theories. In this work, we calculate the bipartition entanglement entropy for this class of models. Our formalism allows us to do most of the calculation for arbitrary dimension d. We show that the entanglement entropy S_A in a sub-region A is proportional to log(GSD_Ã ), where GSD_Ã is the ground state degeneracy of a particular restriction of the full model to A. When A has the topology of a d-dimensional ball, the GSD_Ã counts the number of edge states. In this case, S A scales with the area of the (d 1)-dimensional boundary of A. The precise formula for the entropy we obtain is in agreement with entanglement calculations for known topological models.
 
WARNING - Viewing this document is conditioned on your acceptance of the following terms of use:
This document is only for private use for research and teaching activities. Reproduction for commercial use is forbidden. This rights cover the whole data about this document as well as its contents. Any uses or copies of this document in whole or in part must include the author's name.
phd.pdf (1.82 Mbytes)
Publishing Date
2019-12-20
 
WARNING: Learn what derived works are clicking here.
All rights of the thesis/dissertation are from the authors
CeTI-SC/STI
Digital Library of Theses and Dissertations of USP. Copyright © 2001-2021. All rights reserved.