Symmetry reduction induced by anyon condensation: a tensor network approach

Abstract

Topological ordered phases are related to changes in the properties of their quasi-particle excitations (anyons). We study these relations in the framework of projected entanglement pair states (\textsf{PEPS}) and show how condensing and confining anyons reduces a local gauge symmetry to a global on-site symmetry. We also study the action of this global symmetry over the quasiparticle excitations. As a byproduct, we observe that this symmetry reduction effect can be applied to one-dimensional systems as well, and brings about appealing physical interpretations on the classification of phases with symmetries using matrix product states (\textsf{MPS}). The case of ${\mathbb{Z}}_2$ on-site symmetry is studied in detail.

21+5 pages, 15+3 figures. Introduction and conclusions enlarged, references and figure added, minor typos corrected, appendix about dyons added

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• Classification of phases for mixed states via fast dissipative evolution
• Subsystem symmetry enriched topological order in three dimensions
• Complete characterization of non-Abelian topological phase transitions and detection of anyon splitting with projected entangled pair states
• On the stability of topological order in tensor network states
• Quantum phase transition between symmetry enriched topological phases in tensor-network states
• Fractionalization of subsystem symmetries in two dimensions
• Local order parameters for symmetry fractionalization
• String order parameters for symmetry fractionalization in an enriched toric code
• Detecting transition between Abelian and non-Abelian topological orders through symmetric tensor networks