TY - JOUR
T1 - Interacting fermionic symmetry-protected topological phases in two dimensions
AU - Wang, Chenjie
AU - Lin, Chien-Hung
AU - Gu, Zheng-Cheng
PY - 2017/5/15
Y1 - 2017/5/15
N2 - We classify and construct models for two-dimensional (2D) interacting fermionic symmetry-protected topological (FSPT) phases with general finite Abelian unitary symmetry Gf. To obtain the classification, we couple the FSPT system to a dynamical discrete gauge field with gauge group Gf and study braiding statistics in the resulting gauge theory. Under reasonable assumptions, the braiding statistics data allows us to infer a potentially complete classification of 2D FSPT phases with Abelian symmetry. The FSPT models that we construct are simple stacks of the following two kinds of existing models: (i) free-fermion models and (ii) models obtained through embedding of bosonic symmetry-protected topological (BSPT) phases. Interestingly, using these two kinds of models, we are able to realize almost all FSPT phases in our classification, except for one class. We argue that this exceptional class of FSPT phases can never be realized through models (i) and (ii), and therefore can be thought of as intrinsically interacting and intrinsically fermionic. The simplest example of this class is associated with Zf4 × Z4 × Z4 symmetry. In addition, we show that all 2D FSPT phases with a finite Abelian symmetry of the form Zf2×G can be realized through the above models (i), (ii), or a simple stack of them. Finally, we study the stability of BSPT phases when they are embedded into fermionic systems.
AB - We classify and construct models for two-dimensional (2D) interacting fermionic symmetry-protected topological (FSPT) phases with general finite Abelian unitary symmetry Gf. To obtain the classification, we couple the FSPT system to a dynamical discrete gauge field with gauge group Gf and study braiding statistics in the resulting gauge theory. Under reasonable assumptions, the braiding statistics data allows us to infer a potentially complete classification of 2D FSPT phases with Abelian symmetry. The FSPT models that we construct are simple stacks of the following two kinds of existing models: (i) free-fermion models and (ii) models obtained through embedding of bosonic symmetry-protected topological (BSPT) phases. Interestingly, using these two kinds of models, we are able to realize almost all FSPT phases in our classification, except for one class. We argue that this exceptional class of FSPT phases can never be realized through models (i) and (ii), and therefore can be thought of as intrinsically interacting and intrinsically fermionic. The simplest example of this class is associated with Zf4 × Z4 × Z4 symmetry. In addition, we show that all 2D FSPT phases with a finite Abelian symmetry of the form Zf2×G can be realized through the above models (i), (ii), or a simple stack of them. Finally, we study the stability of BSPT phases when they are embedded into fermionic systems.
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U2 - 10.1103/PhysRevB.95.195147
DO - 10.1103/PhysRevB.95.195147
M3 - 21_Publication in refereed journal
VL - 95
JO - Physical Review B: covering condensed matter and materials physics
JF - Physical Review B: covering condensed matter and materials physics
SN - 2469-9950
IS - 19
M1 - 195147
ER -