Entanglement spectrum of a topological phase in one dimension

Details Entanglement spectrum of a topological phase in one dimension Entanglement spectrum of a topological phase in one dimension

2009-10-09

arxiv.org/abs/0910.1811v2

Phys. Rev. B 81, 064439 (2010)

Physics

Condensed Matter

Strongly Correlated Electrons

11 pages, 4 figures, references added, minor corrections, meta data updated

Scientific paper

10.1103/PhysRevB.81.064439

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 $\pi$-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.

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