PIRSA:13030116 Scientific Series Condensed Matter

DOI10.48660/13030116

Series: Quantum Matter

Hermele, M. (2013). Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions. Perimeter Institute. https://pirsa.org/13030116

Hermele, Michael. Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions. Perimeter Institute, Mar. 26, 2013, https://pirsa.org/13030116 

@misc{ pirsa_PIRSA:13030116,
  doi = {10.48660/13030116},
  url = {https://pirsa.org/13030116},
  author = {Hermele, Michael},
  keywords = {Condensed Matter},
  language = {en},
  title = {Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions},
  publisher = {Perimeter Institute},
  year = {2013},
  month = {mar},
  note = {PIRSA:13030116 see, \url{https://pirsa.org}}
}

Abstract

Quantum number fractionalization is a remarkable property of topologically ordered states of matter, such as fractional quantum Hall liquids, and quantum spin liquids. For a given type of topological order, there are generally many ways to fractionalize the quantum numbers of a given symmetry. What does it mean to have different types of fractionalization? Are different types of fractionalization a universal property that can be used to distinguish phases of matter? In this talk, I will answer these questions, focusing on a simple class of topologically ordered phases, namely two-dimensional gapped Z2 spin liquids, and I will present a symmetry classification of these phases.  I will also discuss efforts in progress to find microscopic models realizing different symmetry classes.

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