Topological transitions in Kane-Mele-Hubbard ladders

• Autor(a) principal: Magaldi, Rafael Miksian
• Data de Publicação: 2019
• Tipo de documento: Dissertação
• Idioma: eng
• Título da fonte: Biblioteca Digital de Teses e Dissertações da USP
• Texto Completo: https://www.teses.usp.br/teses/disponiveis/43/43134/tde-17092019-140111/
• topic: Density matrix renormalization group; Electronic interactions; Grupo de renormalização da matriz de densidade; Interações eletrônicas; Isolantes topológicos; Kane-Mele-Hubbard; Kane-Mele-Hubbard; Rede de tensores; Tensor networks; Topological insulators

Topological insulators are materials that behave as insulators in the bulk, but present conducting edge states. Despite the growing interest in such materials due to their possible applications on spintronic devices and quantum computing, several open questions still remain regarding the roles of both electronic interactions and dimensionality in these systems. The goal of this work is to tackle some of these questions. To do so, we study a quasi-1D system presenting a topologically non-trivial phase and electronic interactions: the so-called Kane-Mele-Hubbard ladders. Here, we apply the density matrix renormalization group (DMRG) algorithm in the tensor network formalism in order to calculate some physical properties of this system. The DMRG calculations allow us to reach the system\'s ground state and enable the efficient computation of observables and of the entanglement entropy. The Kane-Mele-Hubbard model is an interacting version of the Kane-Mele model, which displays topologically non-trivial phases. The interest on this system is due to the combination of effects caused by the spin-orbit coupling and the electronic interactions. For the non-interacting case we have a topological insulator, whereas in the highly interacting picture we have a Mott insulator with localized electrons. We explore the phase transition between these regimes, looking at the conditions needed for the appearance of spin-polarized edge states. We also propose the entanglement entropy between two halves of the system as an indicator of the topological phase transition, as it presents a particular pattern when the phase transition takes place.