The study of topological phases, which appear in the presence of a strong magnetic field or strong spin-orbit coupling, is a rapidly growing field which involves several fundamental questions and potential applications. As a complement to traditional condensed matter materials, ultracold atoms in optical lattices provide a great tool to explore this physics. They also have some features which require specific theoretical treatment. Various theoretical studies of those systems have been carried out, however, no direct numerical simulations has been undertaken yet.
Here we propose to implement a Density Matrix Renormalization Group (DMRG) approach to study topological phases of ultracold atoms in two dimensions. Such direct numerical simulations will permit to give an accurate quantitative description of those systems, that will improve our theoretical understanding and help the analysis of the experiments. We also propose a collaboration with an experimental group.
This project is relevant to current research efforts, ambitious, timely and in relation with the state-of-the-art for what concerns the system under study, the numerical technique that will be used and the experiments that are concerned. It will create a unique synergy at the European level between the French research community of ultracold atoms (where the fellow comes from) and the Munich area which is at the forefront for both DMRG methods (in the host group) and experimental techniques (in the collaborating group). Eventually, through this project, the fellow will greatly broaden her skills, progressively become independent and acquire an original research profile, thus contributing to her career development.
Call for proposal
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