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It has been known that the topological entanglement entropy is a useful order parameter to detect topologically ordered phases. When global symmetries are imposed, new types of topological phases emerge. They are called symmetry protected topological (SPT) phases for short range entangled states and symmetry enriched topological (SET) phases for long range entangled states. Since the entanglement entropy is insensitive to global symmetries, the topological entanglement entropy is no longer a good order parameter to distinguish SPT and SET phases. In this talk I introduce a new entanglement quantity, a charged entanglement entropy, by grand canonically generalising the entanglement entropy. This charged entanglement entropy is sensitive to global symmetries, and it shows a new universal term, in addition to the topological entanglement entropy, which can be used to distinguish SPT and SET phases.

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Shunji Matsuura, Niels Bohr Institute
Seminar Room 0.03, ETP
Contact: Achim Rosch