Multi-kink topological terms and charge-binding domain-wall condensation induced symmetry-protected topological states: Beyond Chern-Simons/BF theory

Zheng-Cheng Gu Juven Wang Xiao-Gang Wen

Mathematical Physics Theoretical Physics mathscidoc:1904.22005

Phys. Rev. , 2016
Quantum-disordering a discrete-symmetry breaking state by condensing domain-walls can lead to a trivial symmetric insulator state. In this work, we show that if we bind a 1D representation of the symmetry (such as a charge) to the intersection point of several domain walls, condensing such modified domain-walls can lead to a non-trivial symmetry-protected topological (SPT) state. This result is obtained by showing that the modified domain-wall condensed state has a non-trivial SPT invariant -- the symmetry-twist dependent partition function. We propose two different kinds of field theories that can describe the above mentioned SPT states. The first one is a Ginzburg-Landau-type non-linear sigma model theory, but with an additional multi-kink domain-wall topological term. Such theory has an anomalous Uk(1) symmetry but an anomaly-free ZkN symmetry. The second one is a gauge theory, which is beyond Abelian Chern-Simons/BF gauge theories. We argue that the two field theories are equivalent at low energies. After coupling to the symmetry twists, both theories produce the desired SPT invariant.
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@inproceedings{zheng-cheng2016multi-kink,
  title={Multi-kink topological terms and charge-binding domain-wall condensation induced symmetry-protected topological states: Beyond Chern-Simons/BF theory},
  author={Zheng-Cheng Gu, Juven Wang, and Xiao-Gang Wen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190419100952016074254},
  booktitle={Phys. Rev. },
  year={2016},
}
Zheng-Cheng Gu, Juven Wang, and Xiao-Gang Wen. Multi-kink topological terms and charge-binding domain-wall condensation induced symmetry-protected topological states: Beyond Chern-Simons/BF theory. 2016. In Phys. Rev. . http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190419100952016074254.
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