[Seminar] "Exact edge, bulk and bound states of finite topological systems " by Dr. Manuel Valiente from Institute for Advanced Study, Tsinghua University, Beijing, China
Dr. Manuel Valiente
I obtained my PhD at the Humboldt-Universitaet zu Berlin in 2010. I then moved on as a postdoctoral researcher at Aarhus University in Denmark, and spent 6 years as a senior Research Associate at Heriot-Watt University in Edinburgh, Scotland. I am mainly interested in strongly-interacting few- and many-particle quantum systems, especially in reduced dimensions. Ultracold atomic systems, which are nowadays routinely manipulated such that their interactions can become arbitrarily strong, are the main physical systems that motivate my research.
Finite topologically non-trivial systems are often characterised by the presence of bound states at their physical edges. These topological edge modes can be distinguished from usual Shockley waves energetically, as their energies remain finite and in-gap. We put forward a method for obtaining the spectrum and wave functions of topological edge modes for arbitrary finite lattices, including the incommensurate case. A small number of parameters are easily determined numerically, with the form of the eigenstates remaining fully analytical. We also obtain the bulk modes in the finite system analytically and their eigenenergies, which lie within the infinite-size limit continuum. Our method is general and can be easily applied to obtain the properties of non-topological models and/or extended to include impurities.