dc.description.abstract
In recent years, there has been a lot of work, that has focused on studying Ising spin chains with tunable long-range interactions. Such chains can now, for instance, be experimentally realized using ultracold atoms or in trapped ions coupled to vibrational degrees of freedom, etc. Contrary to what happens in short range systems, the primary theoretical and experimental interests, are in studying the novel static and dynamic phenomena that occur here, such as the possible violation of the area law of the ground state entanglement entropy in one dimension, or the non-local propagation of correlations. While some of the local properties can still be approximately understood theoretically via conventional analytical and numerical methods, it is quite challenging to determine generic properties of long-range interacting systems, more so when global or topological properties needs to be uncovered. To facilitate further understandings, a theoretical model, dealing with long range topological superconducting pairings has very recently been proposed [PRL 113, 156402] with complete analytical tractability. In this thesis, we would try to propose ways to experimentally realise this specific model in solid state settings or alternatively in quantum simulators of ultracold atoms or trapped ions, as a way to enhance and complement our analytical understandings about the robustness of the topological superconducting phase.
