Parafermionic edge zero modes in Zn-invariant spin chains

By P. Fendley. 2012

278 citations recorded by the source corpus.

A sign of topological order in a gapped one-dimensional quantum chain is the existence of edge zero modes. These occur in the Z2-invariant Ising/Majorana chain, where they can be understood using free-fermion techniques. Here I discuss their presence in spin chains with Zn symmetry, and prove that for appropriate couplings they are exact, even in this strongly interacting system. These modes are naturally expressed in terms of parafermions, generalizations of fermions to the Zn case. I show that parafermionic edge zero modes do not occur in the usual ferromagnetic and antiferromagnetic cases, but rather only when the interactions are chiral, so that spatial-parity and time-reversal symmetries are broken.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/88711d6002646b9079f1cb400e25d6672db85054

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. J. Alicea
2. R. Verresen
3. Matthew Fisher
4. Romain Vasseur
5. Frank Pollmann
6. N. Lindner
7. A. Stern
8. C. Nayak

In Condensed Matter Physics

1. R. Verresen
2. J. Alicea
3. Frank Pollmann
4. Romain Vasseur
5. D. Parker
6. Thomas Scaffidi
7. Roger S. K. Mong
8. A. Stern

Citations in the corpus

• Universal topological quantum computation from a superconductor/Abelian quantum Hall heterostructure (2013, methodology): “Domain walls separating physically distinct gapped regions bind Zn generalizations of Majorana zero modes [87,88] and consequently realize nonAbelian anyons of a more interesting variety than those in a 1D p-wave superconductor.”
• Gapless Symmetry-Protected Topological Order (2017, background): “[89] Paul Fendley, “Parafermionic edge zero modes in Zninvariant spin chains,” Journal of Statistical Mechanics: Theory and Experiment 2012, P11020 (2012).”
• Statistical localization: From strong fragmentation to strong edge modes (2019, background): “[53] Paul Fendley, “Parafermionic edge zero modes inZninvariant spin chains,” Journal of Statistical Mechanics: Theory and Experiment 2012, P11020 (2012).”