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Universidade Estadual de Campinas Instituto de Física Gleb Wataghin Bruno Ricardi de Abreu Quenches numéricos de desordem no modelo Bose-Hubbard Numerical quenches of disorder in the Bose-Hubbard model CAMPINAS 2018 Bruno Ricardi de Abreu Numerical quenches of disorder in the Bose-Hubbard model Quenches numéricos de desordem no modelo Bose-Hubbard Tese apresentada ao Instituto de Física Gleb Wa- taghin da Universidade Estadual de Campinas como parte dos requisitos exigidos para a obten- ção do título de Doutor em Ciências. Thesis presented to the Institute of Physics Gleb Wataghin of the University of Campinas in par- tial fulfillment of the requirements for the degree of Doctor in Sciences. Orientador: Silvio Antonio Sachetto Vitiello Este exemplar corresponde à versão final da tese defendida pelo aluno Bruno Ricardi de Abreu, e orientada pelo Prof. Dr. Silvio An- tonio Sachetto Vitiello. Campinas 2018 Agência(s) de fomento e nº(s) de processo(s): CNPq, 141252/2014-0; CNPq, 232682/2014-3 ORCID: ttps://orcid.org/0000-0002-9067-779X Ficha catalográfica Universidade Estadual de Campinas Biblioteca do Instituto de Física Gleb Wataghin Lucimeire de Oliveira Silva da Rocha - CRB 8/9174 Abreu, Bruno Ricardi de, 1990- Ab86n AbrNumerical quenches of disorder in the Bose-Hubbard model / Bruno Ricardi de Abreu. – Campinas, SP : [s.n.], 2018. AbrOrientador: SIlvio Antonio Sachetto Vitiello. AbrTese (doutorado) – Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin. Abr1. Superfluidez. 2. Bose-Hubbard, Modelo de. 3. Monte Carlo quântico, Método de. 4. Sistemas desordenados. 5. Átomos ultrafrios. I. Vitiello, Silvio Antonio Sachetto, 1950-. II. Universidade Estadual de Campinas. Instituto de Física Gleb Wataghin. III. Título. Informações para Biblioteca Digital Título em outro idioma: Quenches numéricos de desordem no modelo Bose-Hubbard Palavras-chave em inglês: Superfluidity Bose-Hubbard model Quantum Monte Carlo method Disordered systems Ultracold atoms Área de concentração: Física Titulação: Doutor em Ciências Banca examinadora: Silvio Antonio Sachetto Vitiello Ricardo Luis Doretto Marcos Cesar de Oliveira Raimundo Rocha dos Santos José Abel Hoyos Neto Data de defesa: 08-08-2018 Programa de Pós-Graduação: Física Powered by TCPDF (www.tcpdf.org) MEMBROS DA COMISSÃO JULGADORA DA TESE DE DOUTORADO DE BRUNO RICARDI DE ABREU RA: 80858 APRESENTADA E APROVADA AO INSTITUTO DE FÍSICA “GLEB WATAGHIN”, DA UNIVERSIDADE ESTADUAL DE CAMPINAS, EM 08/08/2018. COMISSÃO JULGADORA: - Prof. Dr. Silvio Antonio Sachetto Vitiello - (Orientador) - IFGW/UNICAMP - Prof. Dr. Ricardo Luis Doretto - IFGW/UNICAMP - Prof. Dr. Marcos Cesar de Oliveira - IFGW/UNICAMP - Prof. Dr. Raimundo Rocha dos Santos - INSTITUTO DE FÍSICA - UFRJ - Prof. Dr. José Abel Hoyos Neto - INSTITUTO DE FÍSICA/SÃO CARLOS A Ata de Defesa, assinada pelos membros da Comissão Examinadora, consta no processo de vida acadêmica do aluno. CAMPINAS 2018 Acknowledgements My entire career as a physics student and, in particular, the work that is presented in this dissertation could not be possibly made without the unconditional love and support that I have always received from my family. I feel like just thanking them on these lines does not even fairly compensate for the most elemental source of motivation that they represent to me. Even so, if not by other means, I express here my gratefulness for having them in my life. It is an extraordinarily comforting pleasure to be sure that they will always be by side no matter the possible different courses that my life would take as a consequence of my choices. Just as important as them for the construction of my career as a physicist, the development of this work, and for my formation as a citizen and human being during my time as a student at Unicamp is my long-term advisor Silvio Vitiello. Along our journey he has consistently been aware of my feelings, tempering my thoughts when they were too fast and confusing, hastening my ideas when I was moving too slow and wisely advising me in a number of situations of life with distinguished discernment and sagacity. I am deeply thankful for his unrestricted patience and perseverance during this period. I am also very gratified for people that work at IFGW/Unicamp and made this project possible. From faculty, with highly skilled professors that taught me physics on the finest level, to staff that provided fundamental support such as access to scientific books and articles through the library (BIF), scheduling of classrooms for presentations whenever needed and so many other things, including hot, good coffee and snacks. I am completely sure that they made academic lifehere a lot easier for me. I must also recognize that this research used the computing resources and assistance of the John David Rogers Computing Center (CCJDR) in IFGW, whose staff has been extremelly supportive as well. Part of this work was made in the United States, more specifically at the University of Illinois at Urbana-Champaing (UIUC), Institute for Condensed Matter Theory (ICMT), where I have been a visiting scholar with Professor David Ceperley. He has demonstrated that, much more than the extraordinary scientist that his career grants, he is an excellent human being. He helped me by being kind and prestative, keeping my hopes alive during what was, beyond any doubts, the hardest piece of my life so far. I am deeply grateful for his support, which of course extended to academic and research life. During this period I also met Ushnish Ray, an excepetionally talented scientist that has guided me through the subtleties of the subjects and methods that were used throughout this work. I am thankful for his patience, consideration and collaboration. Last, but not least, I shall say that I have been exceedingly lucky in finding new friends and keeping old ones during these years, both in Brasil and in the United States. Their friendship is priceless and makes life worth living. During my time in the US, I met my beloved Kinsey who has, since then, sweetened my life with unequivocal love, support and kindness, softening my heart whenever my hard thoughts were overcoming my feelings. I am thankful for financial support from the Conselho Nacional de Desenvolvimento Científico e Tecnológico – CNPq under grants No. 141242/2014-0 and No. 232682/2014-3 that concern both regular doctorate scholarship and the Science Without Borders program. Resumo Neste trabalho as propriedades das fases superfluida (SF) e vidro de Bose (BG) do modelo Bose-Hubbard desordenado em três dimensões são investigadas usando simulações de Monte Carlo quântico. O diagrama de fases é construído utilizando desordem Gaussiana nas energias de ocu- pação, e dois tipos adicionais de distribuição, exponencial e uniforme, são estudados com respeito às suas influências quantitativas e qualitativas no estabelecimento do super-fluxo que caracteriza o estado superfluido. A estatística de observáveis do sistema pertinente a distribuições depro- babilidade sobre o ensemble de desordem são estudadas para diversos valores de interação entre átomos e tamanhos da rede, onde fortes efeitos de tamanho são observados. Estes efeitos estão relacionados ao mecanismo que dirige a transição SF-BG e corroboram o entendimento do caráter percolativo da transição. Apesar disso, ambos os parâmetros de ordem, a fração de superfluido e a compressibilidade, permanecem auto-promediantes por toda fase superfluida. Nos arredores do contorno SF-BG, efeitos de tamanho são dominantes mais ainda sugerem que a auto-promediação persiste. Estes resultados são relevantes para experimentos com gases atômicos ultrafrios onde um procedimento sistemático de mediação sobre realizações de desordem não é tipicamente possível, e também para cálculos numéricos que precisam necessariamente considerar efeitos de tamanho quando o sistema apresenta pequenas quantidades de superfluido. Palavras-chave: superfluidez, Monte Carlo quântico, modelo de Bose-Hubbard, desordem, vi- dro de Bose, percolação, auto-promediação, modelo de Bose-Hubbard desordenado, gases atômicos ultrafrios Abstract In this work the properties of the superfluid (SF) and Bose-glass (BG) phases in the three- dimensional disordered Bose-Hubbard model are investigated using Quantum Monte-Carlo simu- lations. The phase diagram is generated using Gaussian disorder on the on-site potential, and two additional types of distributions, namely exponential and uniform, are studied regarding both their qualitative and quantitative influence on the establishment of the superflow that characterizes the superfluid state. Statistics pertaining to probability distributions of observables over the disorder ensemble are studied for a range of interaction strengths and system sizes, where strong finite-size effects are observed. These effects are related to the mechanism that drives the SF-BG transition and corroborates the understanding of the percolation character of the transition. Despite this, both order parameters, the superfluid fraction and compressibility, remain self-averaging through- out the superfluid phase. Close to the superfluid-Bose-glass phase boundary, finite-size effects dominate but still suggest that self-averaging holds. These results are pertinent to experiments with ultracold atomic gases where a systematic disorder averaging procedure is typically not pos- sible, and also to numerical calculations that must necessarily address finite-size effects when the system exhibits small amounts of superfluid. Keywords: superfluidity, Quantum Monte
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