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Fermion condensation and super pivotal categories

Aasen, David and Lake, Ethan and Walker, Kevin (2017) Fermion condensation and super pivotal categories. . (Submitted)

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We study fermionic topological phases using the technique of fermion condensation. We give a prescription for performing fermion condensation in bosonic topological phases which contain a 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. There are two distinct types of objects in fermionic theories, which we call "m-type" and "q-type" particles. The endomorphism algebras of q-type particles are complex Clifford algebras, and they have no analogues in bosonic theories. We construct a fermionic generalization of the tube category, which allows us to compute the quasiparticle excitations in fermionic topological phases. We then prove a series of results relating data in condensed theories to data in their parent theories; for example, if C is a modular tensor category containing a fermion, then the tube category of the condensed theory satisfies Tube(C/ψ)≅C×(C/ψ). We also study how modular transformations, fusion rules, and coherence relations are modified in the fermionic setting, prove a fermionic version of the Verlinde dimension formula, construct a commuting projector lattice Hamiltonian for fermionic theories, and write down a fermionic version of the Turaev-Viro-Barrett-Westbury state sum. A large portion of this work is devoted to three detailed examples of performing fermion condensation to produce fermionic topological phases: we condense fermions in the Ising theory, the SO(3)_6 theory, and the 1/2E_6 theory, and compute the quasiparticle excitation spectrum in each of these examples.

Item Type:Report or Paper (Discussion Paper)
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Additional Information:Ethan Lake and Dave Aasen are grateful to Nick Bultinck, Nicolas Tarantino, Ryan Thorngren, Brayden Ware, and Dominic Williamson for helpful discussions. Dave Aasen thanks Parsa Bonderson for explaining his unpublished work at early stages of this project. Dave Aasen gratefully acknowledges support from the KITP Graduate Fellows Program, the National Science Foundation through grant DMR- 1723367 and the Caltech Institute for Quantum Information and Matter, an NSF Physics Frontiers Center with support of the Gordon and Betty Moore Foundation through Grant GBMF1250. Ethan Lake is supported by the Fannie and John Hertz Foundation. Dave Aasen and Ethan Lake acknowledge support by the 2016 Boulder Summer School for Condensed Matter and Materials Physics through NSF grant DMR-13001648. Kevin Walker thanks Zhenghan Wang and Scott Morrison for helpful conversations, and thanks the Aspen Center for Physics and the Mathematisches Forschungsinstitut Oberwolfach for providing stimulating research environments.
Group:IQIM, Institute for Quantum Information and Matter
Funding AgencyGrant Number
Kavli Institute for Theoretical PhysicsUNSPECIFIED
Institute for Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationGBMF1250
Fannie and John Hertz FoundationUNSPECIFIED
Record Number:CaltechAUTHORS:20180129-085443018
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84555
Deposited By: Tony Diaz
Deposited On:31 Jan 2018 19:07
Last Modified:03 Oct 2019 19:19

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