Entanglement spectrum of a topological phase in one dimension

Frank Pollmann, Ari M. Turner, Erez Berg, Masaki Oshikawa

Research output: Contribution to journalArticlepeer-review

974 Scopus citations

Abstract

We show that the Haldane phase of S=1 chains is characterized by a double degeneracy of the entanglement spectrum. The degeneracy is protected by a set of symmetries (either the dihedral group of π rotations about two orthogonal axes, time-reversal symmetry, or bond centered inversion symmetry), and cannot be lifted unless either a phase boundary to another, "topologically trivial," phase is crossed, or the symmetry is broken. More generally, these results offer a scheme to classify gapped phases of one-dimensional systems. Physically, the degeneracy of the entanglement spectrum can be observed by adiabatically weakening a bond to zero, which leaves the two disconnected halves of the system in a finitely entangled state.

Original languageEnglish
Article number064439
JournalPhysical Review B - Condensed Matter and Materials Physics
Volume81
Issue number6
DOIs
StatePublished - 26 Feb 2010
Externally publishedYes

Fingerprint

Dive into the research topics of 'Entanglement spectrum of a topological phase in one dimension'. Together they form a unique fingerprint.

Cite this