Fermionic Symmetry Protected Topological Phase Induced by Interaction Shangqiang NING First year PHD student Institute For Advanced Study, Tsinghua University.

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Presentation transcript:

Fermionic Symmetry Protected Topological Phase Induced by Interaction Shangqiang NING First year PHD student Institute For Advanced Study, Tsinghua University

Collaborators Hongchen Jiang Slac, Stanford Zhengxin Liu IASTU, Beijing

Outline 1. Background and motivation 2. Study of a specific model 3. Conclusion

Background and Motivation 2D topological insulator Key properties of TI: Band insulator Mass terms breaks T breaks U(1) X. Qi, S.C. Zhang RevModPhys

Symmetry Protected Topological phase (SPT phase) gapped gapless

Classification of SPT For more symmetry group in

∎ SPT phases also exist in Bosonic systems S=1 Haldane phase (Bosonic) Finite excitation gap No symmetry breaking SO(3) symmetry protected spin-1/2 edge states Degeneracy of entanglement spectrum Spin-1/2 Spin-1 Haldane 83; Affleck, Kennedy, Lieb, Tasaki 87 Gu, Wen 09; Pollmann et.al 09; Chen,Gu,Wen 11 bulk gap SO(3) symmetry

A B

Entanglement spectrum J 2 /J 1 =0.9 SO(3) symmetry Non trivial Trivial

Classification of Bosonic SPT SO(3) symmetry : 2 phases Xie Chen, Zheng-Cheng Gu, and Xiao-Gang Wen,2011

Classification of Interacting Fermionic SPT 1D superconductor 2D superconductor Time reversal and mirror reflect ZZ8Z8 It seems that interactions reduce the classification. However, it maybe not true! Hong Yao and Shinsei Ryu, arXiv : Evelyn Tang and Xiao-Gang Wen arXiv: v2

Model

Symmetry and classification free case, only the trivial phase. 2 projective representation  two SPT phases.

Non-interacting limit U=0, J=0 = 2-fold

Non-interacting limit U=0, J=0 SPT only focus on gapped phases. Open boundary, no zero mode, indicating the trivialness of phase

Add Hubbard interaction the band insulator and the Mott insulator are adiabatically connected

Interacting case

Competition

Interacting case

We find two phases in the interacting case ： trivial insulator and Haldane insulator

Conclusion

Thanks for your attention!