Multipolar topological field theories: Bridging higher order topological insulators and fractons

Yizhi You, F. J. Burnell, Taylor L. Hughes

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29 Scopus citations


Two new recently proposed classes of topological phases, namely, fractons and higher order topological insulators (HOTIs), share at least superficial similarities. The wide variety of proposals for these phases calls for a universal field theory description that captures their key characteristic physical phenomena. In this work, we construct topological multipolar response theories that capture the essential features of some classes of fractons having subsystem symmetries and higher order topological insulators. Remarkably, we find that despite their distinct symmetry structure, some classes of fractons and HOTIs can be connected through their essentially identical topological response theories. More precisely, we propose a topological quadrupole response theory that describes both a 2D symmetry-protected fracton phase and a related bosonic quadrupolar HOTI with strong interactions. Such a topological quadrupole term encapsulates the protected corner charge modes and, for the HOTI, also determines an anomalous edge with a fractional dipole moment. In 3D, we propose a dipolar Chern-Simons theory with a quantized coefficient as a description of the response of both second-order HOTIs harboring chiral hinge currents and of a related fracton phase. This theory correctly predicts chiral currents on the hinges and anomalous dipole currents on the surfaces. We generalize these results to higher dimensions to reveal a family of multipolar Chern-Simons terms and related θ-term actions that can be reached via dimensional reduction or extension from the Chern-Simons theories.

Original languageEnglish (US)
Article number245128
JournalPhysical Review B
Issue number24
StatePublished - Jun 15 2021

Bibliographical note

Funding Information:
We are grateful to Titus Neupert, Mike Stone, and Chong Wang for insightful comments and discussions. Y.Y. is supported by PCTS Fellowship at Princeton University. FJB is grateful for the financial support of NSF-DMR 1352271 and the Sloan Foundation FG-2015-65927. Y.Y. and T.L.H. are supported in part by the National Science Foundation under Grant No. NSF PHY-1748958(KITP) during the Topological Quantum Matter program. T.L.H. thanks the US National Science Foundation under grant DMR 1351895-CAR, and the MRSEC program under NSF Award No. DMR-1720633 (SuperSEED) for support. This work (Y.Y., F.J.B., and T.L.H.) was initiated at Aspen Center for Physics, which is supported by National Science Foundation grant PHY-1607611.

Publisher Copyright:
© 2021 American Physical Society.


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