Fermionic symmetry protected topological phases and cobordisms

Kapustin, Anton; Thorngren, Ryan; Turzillo, Alex; Wang, Zitao

doi:10.1007/JHEP12(2015)052

Title: Fermionic symmetry protected topological phases and cobordisms

Journal Article · 10 December 2015 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/JHEP12(2015)052 · OSTI ID:1599360

Kapustin, Anton ^[1]; Thorngren, Ryan ^[2]; Turzillo, Alex ^[1]; Wang, Zitao ^[1]

California Inst. of Technology (CalTech), Pasadena, CA (United States)
Univ. of California, Berkeley, CA (United States)

It has been proposed recently that interacting Symmetry Protected Topological Phases can be classified using cobordism theory. We test this proposal in the case of Fermionic SPT phases with $ {\mathrm{\mathbb{Z}}}_2 $ symmetry, where $ {\mathrm{\mathbb{Z}}}_2 $ is either time-reversal or an internal symmetry. We find that cobordism classification correctly describes all known Fermionic SPT phases in space dimension D ≤ 3 and also predicts that all such phases can be realized by free fermions. In higher dimensions we predict the existence of inherently interacting fermionic SPT phases

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Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0011632; FG02-92ER40701

OSTI ID:: 1599360

Journal Information:: Journal of High Energy Physics (Online), Vol. 2015, Issue 12; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 187 works

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