Entanglement spectrum classification of Cn-invariant noninteracting topological insulators in two dimensions

Chen Fang, Matthew J. Gilbert, B. Andrei Bernevig

Research output: Contribution to journalArticlepeer-review

55 Scopus citations


We study the single-particle entanglement spectrum in 2D topological insulators which possess n-fold rotation symmetry. By defining a series of special choices of subsystems on which the entanglement is calculated, or real space cuts, we find that the number of protected in-gap states for each type of these real space cuts is a quantum number indexing (if any) nontrivial topology in these insulators. We explicitly show that the number of protected in-gap states is determined by a Zn index (z1,...,zn), where zm is the number of occupied states that transform according to mth one-dimensional representation of the Cn point group. We find that for a space cut separating 1/pth of the system, the entanglement spectrum contains in-gap states pinned in an interval of entanglement eigenvalues [1/p,1-1/p]. We determine the number of such in-gap states for an exhaustive variety of cuts, in terms of the Zn index. Furthermore, we show that in a homogeneous system, the Zn index can be determined through an evaluation of the eigenvalues of point-group symmetry operators at all high-symmetry points in the Brillouin zone. When disordered n-fold rotationally symmetric systems are considered, we find that the number of protected in-gap states is identical to that in the clean limit as long as the disorder preserves the underlying point-group symmetry and does not close the bulk insulating gap.

Original languageEnglish (US)
Article number035119
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number3
StatePublished - Jan 14 2013

All Science Journal Classification (ASJC) codes

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics


Dive into the research topics of 'Entanglement spectrum classification of C<sub>n</sub>-invariant noninteracting topological insulators in two dimensions'. Together they form a unique fingerprint.

Cite this