TITLE: Low-dimensional topological insulators: flat bands, exotic symmetries and quantum information applications
AUTHOR: Juan Zurita
SUPERVISED BY: Gloria Platero Coello (ICMM) and Charles Creffield (UCM)
WHEN: 28 de noviembre, a las 12PM
WHERE: Sala de Grados, Facultad de Ciencias Físicas UCM
ABSTRACT: In this thesis, we study quasi-one-dimensional topological insulators, with an emphasis on their symmetries and applications to quantum information. We focus on the in-depth analysis of the Creutz ladder tight-binding model, a crossed-linked ladder immersed in a magnetic field. We discuss its phase diagram, edge states, experimental implementations, and the effect of interactions.
In it, we find and investigate an unusual type of chiral symmetry that can act together with more standard symmetries to protect the edge states. This occurs at points in the phase diagram where the bands of the model are flat due to magnetic interference. Inspired by this, we define other cross-linked ladder models with flat bands that also have unconventional symmetries.
Finally, we study systems with several different topological regions separated by domain walls. These walls also house topological boundary states, like the ends of the model. We consider a multidomain Creutz ladder and two simpler models, and we propose particle transfer protocols between any two of the boundaries. The domain walls can be used as amplifiers in the transfer, dramatically increasing its speed and robustness. We use these protocols to prepare two- and three-qubit maximally entangled states.
