PIRSA:18100047 Scientific Series Condensed Matter

DOI10.48660/18100047

Series: Colloquium

Shapourian, H. (2018). Topological invariants and entanglement negativity in SPT phases of fermions . Perimeter Institute. https://pirsa.org/18100047

Shapourian, Hassan. Topological invariants and entanglement negativity in SPT phases of fermions . Perimeter Institute, Oct. 04, 2018, https://pirsa.org/18100047 

@misc{ pirsa_PIRSA:18100047,
  doi = {10.48660/18100047},
  url = {https://pirsa.org/18100047},
  author = {Shapourian, Hassan},
  keywords = {Condensed Matter},
  language = {en},
  title = {Topological invariants and entanglement negativity in SPT phases of fermions },
  publisher = {Perimeter Institute},
  year = {2018},
  month = {oct},
  note = {PIRSA:18100047 see, \url{https://pirsa.org}}
}

Abstract

Searching for a proper set of order parameters which distinguishes different phases of matter sits in the heart of condensed matter physics. In this talk, I discuss topological invariants as (non-local) order parameters for symmetry protected topological (SPT) phases of fermions in the presence of time-reversal symmetry. It turns out that topological invariants provide a natural definition for the partial transpose of density matrices. The partial transpose can then be used to define an entanglement measure (analog of entanglement negativity) for mixed states of fermions. I will show that this quantity captures the mixed state entanglement in fermionic SPTs as well as in a system of free fermions with a Fermi surface.

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