PIRSA:10120024

Classifying Topological Order: Dualities and Hierarchies

Buerschaper, O. (2010). Classifying Topological Order: Dualities and Hierarchies. Perimeter Institute. https://pirsa.org/10120024

Buerschaper, Oliver. Classifying Topological Order: Dualities and Hierarchies. Perimeter Institute, Dec. 06, 2010, https://pirsa.org/10120024 

          @misc{ pirsa_PIRSA:10120024,
            doi = {10.48660/10120024},
            url = {https://pirsa.org/10120024},
            author = {Buerschaper, Oliver},
            keywords = {Quantum Information},
            language = {en},
            title = {Classifying Topological Order: Dualities and Hierarchies},
            publisher = {Perimeter Institute},
            year = {2010},
            month = {dec},
            note = {PIRSA:10120024 see, \url{https://pirsa.org}}
          }

Oliver Buerschaper

Multiverse Computing (Germany)

Talk number
PIRSA:10120024
Collection
Talk Type
Subject
Abstract
Topological order is a new kind of collective order which appears in two-dimensional quantum systems such as the fractional quantum Hall effect and brings about rather unusual particles: unlike bosons or fermions these anyons obey exotic statistics and can be exploited to perform quantum computation. Topological order also implies that quantum states at low energies exhibit a very subtle, yet intricate inner structure. Remarkably, both phenomena can be studied in relatively simple spin systems (like Kitaev's quantum double models and the ubiquitous toric code) which in fact capture the essential properties of entire topological phases of matter in many important cases. What is the relationship between these topological phases? Reviewing recent work I will explain how they arrange themselves in a landscape of dualities and hierarchies. In particular, I will focus on two aspects: first, a duality between electric and magnetic quasiparticles in generalized quantum double models and second, a hierarchy construction of quantum states which are related by the condensation of topological charges.