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Title:
Fermion Condensation and Superconducting String-nets
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Abstract:
We study non-chiral fermionic topological phases through the lens of fermion condensation. We give a prescription for performing fermion condensation in generic bosonic topological phases which contain an emergent fermion. Our approach to fermion condensation can roughly be understood as coupling the parent bosonic topological phase to a phase of physical fermions and condensing pairs of physical and emergent fermions. In contrast to the bosonic fusion categories, the simple objects in the fermionic fusion categories can have endomorphism algebras isomorphic to the complex Clifford algebras. We define a fermionic version of the tube category, providing a framework to investigate the anyonic content of the associated fermionic string-net Hamiltonians. We will highlight generic properties of the fermionic string-nets with several examples.
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