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Braiding Statistics of Vortices in 2+1d Topological Superconductors from Stacking

You, Minyoung (2020) Braiding Statistics of Vortices in 2+1d Topological Superconductors from Stacking. . (Unpublished)

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Class D topological superconductors in 2+1 dimensions are known to have a ℤ₁₆ classification in the presence of interactions, with 16 different topological orders underlying the 16 distinct phases. By applying the fermionic stacking law, which involves anyon condensation, on the effective Hamiltonian describing the topological interaction of vortices in the p+ip superconductor, which generates the 16 other phases, we recover the braiding coefficients of vortices for all remaining phases as well as the ℤ₁₆ group law. We also apply this stacking law to the time-reversal invariant Class DIII superconductors (which can themselves be obtained from stacking two Class D superconductors) and recover their ℤ₂ classification.

Item Type:Report or Paper (Discussion Paper)
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Additional Information:I am grateful to Anton Kapustin for discussions and comments. I would also like to thank Yu-An Chen and Po-Shen Hsin for helpful discussions. The work is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number de-sc0011632.
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Department of Energy (DOE)DE-SC0011632
Record Number:CaltechAUTHORS:20201209-113359742
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:106976
Deposited By: George Porter
Deposited On:09 Dec 2020 21:10
Last Modified:09 Dec 2020 21:10

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