PIRSA:15080116 Scientific Series Condensed Matter

DOI10.48660/15080116

Series: Quantum Matter

(2015). Using anomaly tests to restrict crystal symmetry fractionalization in Z_2 and chiral spin liquids. Perimeter Institute. https://pirsa.org/15080116

Using anomaly tests to restrict crystal symmetry fractionalization in Z_2 and chiral spin liquids. Perimeter Institute, Aug. 11, 2015, https://pirsa.org/15080116 

@misc{ pirsa_PIRSA:15080116,
  doi = {10.48660/15080116},
  url = {https://pirsa.org/15080116},
  author = {},
  keywords = {Condensed Matter},
  language = {en},
  title = {Using anomaly tests to restrict crystal symmetry fractionalization in Z_2 and chiral spin liquids},
  publisher = {Perimeter Institute},
  year = {2015},
  month = {aug},
  note = {PIRSA:15080116 see, \url{https://pirsa.org}}
}

Abstract

Using the method of flux fusion anomaly test recently developed by M. Hermele and X. Chen (arXiv:1508.00573), we show that the possible ways of fractionalize crystal symmetry is greatly restricted if we assume the spin liquid has an SU(2) spin rotation symmetry and the spinon carries a half-integer spin. For a Z_2 spin liquid, under these assumptions the vison can only take the crystal symmetry fractionalization described by the Ising gauge theory. For a chiral spin liquid these assumptions imply that the spinon must also take fractionalized quantum numbers of crystal symmetries.

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