The Density Matrix Renormalization Group Applied to Open Quantum Systems

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 q...

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Bibliographic Details
Author: Casagrande, Heitor Peres
Format: master thesis
Status:Published version
Publication Date:2019
Country:Brasil
Institution:Universidade de São Paulo (USP)
Repository:Biblioteca Digital de Teses e Dissertações da USP
Language:English
OAI Identifier:oai:teses.usp.br:tde-20122019-194947
Online Access:https://www.teses.usp.br/teses/disponiveis/43/43134/tde-20122019-194947/
Access Level:Open access
Keyword: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
Description
Summary: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.