TY - JOUR
T1 - Classification of symmetry-protected phases for interacting fermions in two dimensions
AU - Cheng, Meng
AU - Bi, Zhen
AU - You, Yi Zhuang
AU - Gu, Zheng Cheng
N1 - Funding Information:
We thank Zhenghan Wang and Daniel Freed for enlightening discussions. M.C. would like to thank Parsa Bonderson and Maissam Barkeshli for collaboration on related projects and Perimeter Institute for hospitality where part of the work was done. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research. Z.C.G. also acknowledges startup support from Department of Physics, the Chinese University of Hong Kong, Direct Grant No. 4053224 from the Chinese University of Hong Kong, and the funding from RGC/ECS(No.2191110). Z.B. acknowledges support by the Pappalardo fellowship at MIT.
Publisher Copyright:
© 2018 American Physical Society.
PY - 2018/5/9
Y1 - 2018/5/9
N2 - Recently, it has been established that two-dimensional bosonic symmetry-protected topological (SPT) phases with on-site unitary symmetry G can be completely classified by the group cohomology H3(G,U(1)). Later, group supercohomology was proposed as a partial classification for SPT phases of interacting fermions. In this work, we revisit this problem based on the algebraic theory of symmetry and defects in two-dimensional topological phases. We reproduce the partial classifications given by group supercohomology, and we also show that with an additional H1(G,Z2) structure, a complete classification of SPT phases for two-dimensional interacting fermion systems with a total symmetry group G×Z2f is obtained. We also discuss the classification of interacting fermionic SPT phases protected by time-reversal symmetry.
AB - Recently, it has been established that two-dimensional bosonic symmetry-protected topological (SPT) phases with on-site unitary symmetry G can be completely classified by the group cohomology H3(G,U(1)). Later, group supercohomology was proposed as a partial classification for SPT phases of interacting fermions. In this work, we revisit this problem based on the algebraic theory of symmetry and defects in two-dimensional topological phases. We reproduce the partial classifications given by group supercohomology, and we also show that with an additional H1(G,Z2) structure, a complete classification of SPT phases for two-dimensional interacting fermion systems with a total symmetry group G×Z2f is obtained. We also discuss the classification of interacting fermionic SPT phases protected by time-reversal symmetry.
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U2 - 10.1103/PhysRevB.97.205109
DO - 10.1103/PhysRevB.97.205109
M3 - Article
AN - SCOPUS:85047057966
SN - 2469-9950
VL - 97
JO - Physical Review B-Condensed Matter
JF - Physical Review B-Condensed Matter
IS - 20
M1 - 205109
ER -