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Instituição de Ensino Superior: CENTRO BRASILEIRO DE PESQUISAS FÍSICAS
Programa: FÍSICA (31009018001P5)
Título: On Topological Anderson insulators: from SDRG to machine learning
Autor: MARIA DANIELA LEITE DE SOUZA
Tipo de Trabalho de Conclusão: DISSERTAÇÃO
Data Defesa: 21/05/2019
Resumo:
This thesis is about topological Anderson insulators. It is divided into two parts: one in which we study the so-called Strong Disorder Renormalization Group (SDRG) analysis of a disordered wire, and other in which we use a Neural Network that can recognize topological phases in clean insulators, with possibility of extension to disordered insulators. In the rst part, we start with a review of the basic concepts about Anderson localization and one of the most known models for topological insulators (named the Su-Schriefer-Heeger – SSH – model). Then, we study a disordered wire with chiral symmetry, considering that the usual single parameter scaling hypothesis is violated, and introducing a second scaling parameter. Using the SDRG analysis, we show how to obtain the two-parameter ow diagram for this model. The second part, in its turn, addresses a brief picture to what is a Machine Learning algorithm and more precisely, one with a Feed-forward Neural Network (FNN) architecture. Our starting point is the question of how Machine Learning can be useful to classify topological phases of matter. We found the phase diagram of a clean insulator and extend the analysis for a disordered insulator.

Palavras-Chave: disorder

Abstract: This thesis is about topological Anderson insulators. It is divided into two parts: one in which we study the so-called Strong Disorder Renormalization Group (SDRG) analysis of a disordered wire, and other in which we use a Neural Network that can recognize topological phases in clean insulators, with possibility of extension to disordered insulators. In the rst part, we start with a review of the basic concepts about Anderson localization and one of the most known models for topological insulators (named the Su-Schriefer-Heeger – SSH – model). Then, we study a disordered wire with chiral symmetry, considering that the usual single parameter scaling hypothesis is violated, and introducing a second scaling parameter. Using the SDRG analysis, we show how to obtain the two-parameter ow diagram for this model. The second part, in its turn, addresses a brief picture to what is a Machine Learning algorithm and more precisely, one with a Feed-forward Neural Network (FNN) architecture. Our starting point is the question of how Machine Learning can be useful to classify topological phases of matter. We found the phase diagram of a clean insulator and extend the analysis for a disordered insulator.

Keyword: disorder

Volume: 01
Páginas: 64
Idioma: INGLES
Biblioteca Depositária: CENTRO BRASILEIRO DE PESQUISAS FÍSICAS
Autorização de divulgação: O trabalho possui divulgação autorizada
Anexo: Dissertação Maria Daniela
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