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arXiv · 0910.1811

Entanglement spectrum of a topological phase in one dimension

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

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Frank Pollmann, Erez Berg, Ari M. Turner, Masaki Oshikawa. 2010-04-22. Entanglement spectrum of a topological phase in one dimension. https://doi.org/10.1103/physrevb.81.064439

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