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Disentangling supercohomology symmetry-protected topological phases in three spatial dimensions

Chen, Yu-An and Ellison, Tyler D. and Tantivasadakarn, Nathanan (2020) Disentangling supercohomology symmetry-protected topological phases in three spatial dimensions. . (Unpublished)

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We build exactly solvable lattice Hamiltonians for fermionic symmetry-protected topological (SPT) phases in (3+1)D classified by group supercohomology. A central benefit of our construction is that it produces an explicit finite-depth quantum circuit (FDQC) that prepares the ground state from an unentangled symmetric state. The FDQC allows us to clearly demonstrate the characteristic properties of supercohomology phases - namely, symmetry fractionalization on fermion parity flux loops - predicted by continuum formulations. By composing the corresponding FDQCs, we also recover the stacking relations of supercohomology phases. Furthermore, we derive topologically ordered gapped boundaries for the supercohomology models by extending the protecting symmetries, analogous to the construction of topologically ordered boundaries for bosonic SPT phases. Our approach relies heavily on dualities that relate certain bosonic 2-group SPT phases with supercohomology SPT phases. We develop physical motivation for the dualities in terms of explicit lattice prescriptions for gauging a 1-form symmetry and for condensing emergent fermions. We also comment on generalizations to supercohomology phases in higher dimensions and to fermionic SPT phases outside of the supercohomology framework.

Item Type:Report or Paper (Discussion Paper)
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Chen, Yu-An0000-0002-8810-9355
Additional Information:YC thanks Anton Kapustin, Ryohei Kobayashi, Po-Shen Hsin, and Bowen Yang for many useful discussions. YC was supported in part by the US Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. TDE would like to acknowledge Sujeet Shukla and Lukasz Fidkowski for their work on a preliminary construction of the (3+1)D fSPT models. TDE also thanks Lukasz Fidkowski for carefully explaining the results of Ref. [56], Davide Gaiotto for a useful discussion related to the model in Section III B, and Theo Johnson-Freyd for valuable discussions regarding group supercohomology. TDE is grateful for the hospitality of Perimeter Institute, where much of his work was completed. Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Economic Development, Job Creation and Trade. NT is grateful to Ashvin Vishwanath for helpful discussions and would also like to thank Zheng-Cheng Gu and the participants of the Croucher summer course "Quantum Entanglement and Topological Order" at CUHK for various discussions. NT is supported by NSERC. Part of this work was done during the Simons Collaboration on Ultra Quantum Matter Workshop, which was supported by a grant from the Simons Foundation (651440).
Funding AgencyGrant Number
Department of Energy (DOE)DE-SC0011632
Department of Innovation, Science and Economic Development (Canada)UNSPECIFIED
Ontario Ministry of Economic Development, Job Creation and TradeUNSPECIFIED
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Simons Foundation651440
Record Number:CaltechAUTHORS:20200908-154238572
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:105280
Deposited By: Tony Diaz
Deposited On:08 Sep 2020 22:49
Last Modified:08 Sep 2020 22:49

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