Cluster expansions and the stability of topological phases

          @misc{ pirsa_PIRSA:10050077,
            doi = {10.48660/10050077},
            url = {https://pirsa.org/10050077},
            author = {Klich, Israel},
            keywords = {},
            language = {en},
            title = {Cluster expansions and the stability of topological phases},
            publisher = {Perimeter Institute},
            year = {2010},
            month = {may},
            note = {PIRSA:10050077 see, \url{https://pirsa.org}}
          }
          

Abstract

Anyons are a special kind of excitations which are allowed in two dimensional systems, along with fermions and bosons. The topological nature of braiding of non-abelian anyons may allow a realization of quantum computing gates which is immune to noise. While the insensitivity of the such systems to a localized noise source is a built-in feature, an issue of great importance is more subtle: the robustness to slight deformations of the amiltonian describing the phase by perturbations which are locally tiny but are spread over through the entire system. Such will always arise if the realization of the Hamiltonian in a particular system is not quite perfect. The subject of the talk will be a proof of such stability, and the cluster expansion representation of deformed topological states.