Multikink topological terms and charge-binding domain-wall condensation induced symmetry-protected topological states: Beyond Chern-Simons/BF field theories
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PhysRevB.93.115136.pdf
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Author(s)
Gu, Zheng-Cheng
Wang, Juven C.
Wen, Xiao-Gang
Date Issued
March 2016
Journal
Physical Review B
Publisher
American Physical Society
Citation
Gu, Zheng-Cheng, Juven C. Wang, and Xiao-Gang Wen. “Multikink Topological Terms and Charge-Binding Domain-Wall Condensation Induced Symmetry-Protected Topological States: Beyond Chern-Simons/BF Field Theories.” Physical Review B 93, no. 11 (March 21, 2016). © 2016 American Physical Society
Version
Final published version
Abstract
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 one-dimensional 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 nontrivial symmetry-protected topological (SPT) state. This result is obtained by showing that the modified domain-wall condensed state has a nontrivial 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 nonlinear sigma model theory, but with an additional multikink domain-wall topological term. Such theory has an anomalous U[superscript k](1) symmetry but an anomaly-free Z[k over N] 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.
MIT Department
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.93.115136
