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Topological Quantum Computing Quantum Simulation

Symmetry-enriched topological order in tensor networks: Defects, gauging and anyon condensation

arXiv

Authors: Dominic J. Williamson, Nick Bultinck, Frank Verstraete

Year

2017

Paper ID

24971

Status

Preprint

Abstract Read

~2 min

Abstract Words

106

Citations

N/A

Abstract

We study symmetry-enriched topological order in two-dimensional tensor network states by using graded matrix product operator algebras to represent symmetry induced domain walls. A close connection to the theory of graded unitary fusion categories is established. Tensor network representations of the topological defect superselection sectors are constructed for all domain walls. The emergent symmetry-enriched topological order is extracted from these representations, including the symmetry action on the underlying anyons. Dual phase transitions, induced by gauging a global symmetry, and condensation of a bosonic subtheory, are analyzed and the relationship between topological orders on either side of the transition is derived. Several examples are worked through explicitly.

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We study symmetry-enriched topological order in two-dimensional tensor network states by using graded matrix product operator algebras to represent symmetry induced domain walls.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1711.07982 [2] arXiv https://arxiv.org/abs/1711.07982 [3] Publisher https://arxiv.org/abs/1711.07982

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