PIRSA:15050004

Parafermionic phases with symmetry-breaking and topological order

Alexandradinata, A. (2015). Parafermionic phases with symmetry-breaking and topological order. Perimeter Institute. https://pirsa.org/15050004

Alexandradinata, Aris. Parafermionic phases with symmetry-breaking and topological order. Perimeter Institute, May. 26, 2015, https://pirsa.org/15050004 

          @misc{ pirsa_PIRSA:15050004,
            doi = {10.48660/15050004},
            url = {https://pirsa.org/15050004},
            author = {Alexandradinata, Aris},
            keywords = {Condensed Matter},
            language = {en},
            title = {Parafermionic phases with symmetry-breaking and topological order},
            publisher = {Perimeter Institute},
            year = {2015},
            month = {may},
            note = {PIRSA:15050004 see, \url{https://pirsa.org}}
          }

Aris Alexandradinata Princeton University

DOI 10.48660/15050004
Collection
Talk Type Scientific Series
Subject

Abstract

Parafermions are the simplest generalizations of Majorana fermions that realize topological order. We propose a less restrictive notion of topological order in 1D open chains, which generalizes the seminal work by Fendley [J. Stat. Mech., P11020 (2012)]. The first essential property is that the groundstates are mutually indistinguishable by local, symmetric probes, and the second is a generalized notion of zero edge modes which cyclically permute the groundstates. These two properties are shown to be topologically robust, and applicable to a wider family of topologically-ordered Hamiltonians than has been previously considered. As an application of these edge modes, we formulate a new notion of twisted boundary conditions on a closed chain, which guarantees that the closed-chain groundstate is topological, i.e., it originates from the topological manifold of the open chain. Finally, we generalize these ideas to describe symmetry-breaking phases with a parafermionic order parameter.

These exotic phases are condensates of parafermion multiplets, which generalizes Cooper pairing in superconductors. The stability of these condensates are investigated on both open and closed chains.