| We propose a scheme to classify gapped phases of one dimensional systems in terms of properties of the entanglement spectrum. We discuss the application of this scheme to the classification of phases in two specific examples. The first example is the Haldane phase of S=1 chains. We show that the Haldane phase is protected by certain symmetries and characterized by a double degeneracy of the entanglement spectrum. The degeneracy cannot be lifted unless either a phase boundary to another, "topologically trivial", phase is crossed or the symmetry is broken. In the second example we apply these concepts to classify systems of interacting fermions in one dimension in the presence of time reversal and parity symmetry. |
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