Topological phases are phases of condensed matter that are gapped (require finite energy to be excited from a ground state) and are characterized by numbers or topological invariants related to quantum numbers of their quasiparticle excitations. By the experimental discovery of the fractional quantum Hall effect they came into existence as new phases of matter that support excitations; quasiparticles that accumulate these nontrivial, fixed numbers under the operation of quasiparticle exchange. Due to their topological nature; robustness to any local perturbation the applicability of topological phases is foreseen in the modern field of quantum computing for the storage and manipulation of information by using the braiding rules (the rules of exchange) of quasiparticles of definite, special topological phases
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Our project is a search for stable topological phases, candidates for the computing devices, in the context of multi-component quantum Hall systems and rapidly rotating Fermi gases. Our approach will be mainly numerical based on the long tradition and experience that tell us that detection of topological phases can be trusted on the basis of finite (small) system numerical calculations, but will also use the deep insights that stem from the connection of the topological phases in 2+1 dimension and the quantum field theories in 1+1 dimension.