The Density Matrix Renormalization Group Applied to Open Quantum Systems

• Ano de defesa: 2019
• Autor(a) principal: Casagrande, Heitor Peres
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Cadeias de Spin; Computational Methods; Fenômenos de Transporte; Métodos Computacionais; O Grupo de Renormalização da Matriz Densidade; Open Quantum Systems; Sistemas Quânticos Abertos; Spin Chains; The Density Matrix Renormalization Group; Transport Phenomena
• Link de acesso: https://www.teses.usp.br/teses/disponiveis/43/43134/tde-20122019-194947/

Open quantum systems have been studied for a long time, and albeit theres extensive literature detailing its various aspects, the complexity of the dynamics dictated by the environment and by quantum correlations within the system make it so that much is still unknown. The complexity introduced by quantum correlations instill highly non-trivial features, so that computational simulations are a viable route in studying such systems, which present, as it has been known for a long time, a myriad of rich, interesting phenomena. In this dissertation we implement an open-system version of the density matrix renormalization group, called oDMRG, suited for applications of thermal transport in one-dimensional spin chains. We have successfully implemented a routine to treat a wide range of systems. From the analytical results available for the XXZ model, a bench-mark was made and our results are found to be in agreement with those of previous works, and the simulations are viable in a common desktop computer. This dissertation puts forth the basic tools of oDRMG and may be of use for a variety of future studies in quantum transport and quantum thermodynamics.