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The Density Matrix Renormalization Group Applied to Open Quantum Systems

Casagrande, Heitor Peres

Biblioteca Digital de Teses e Dissertações da USP; Universidade de São Paulo; Instituto de Física 2019-11-06

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  • Título:
    The Density Matrix Renormalization Group Applied to Open Quantum Systems
  • Autor: Casagrande, Heitor Peres
  • Orientador: Landi, Gabriel Teixeira
  • Assuntos: Cadeias De Spin; Fenômenos De Transporte; Métodos Computacionais; O Grupo De Renormalização Da Matriz Densidade; Sistemas Quânticos Abertos; The Density Matrix Renormalization Group; Spin Chains; Open Quantum Systems; Computational Methods; Transport Phenomena
  • Descrição: 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.
  • DOI: 10.11606/D.43.2020.tde-20122019-194947
  • Editor: Biblioteca Digital de Teses e Dissertações da USP; Universidade de São Paulo; Instituto de Física
  • Data de criação/publicação: 2019-11-06
  • Formato: Adobe PDF
  • Idioma: Inglês
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  • Realização: ABCD-USP USP   Logos de Redes Sociais: Freepik

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