Higher-form Gauge Symmetries in Multipole Topological Phases - INSPIRE

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Higher-form Gauge Symmetries in Multipole Topological Phases

Oleg Dubinkin
(
- Illinois U., Urbana
)
,
Alex Rasmussen
(
- Ohio State U.
)
,
Taylor L. Hughes
(
- Illinois U., Urbana
)

Jul 10, 2020

25 pages

Published in:

Annals Phys. 422 (2020) 168297

Published: Nov, 2020

e-Print:

2007.05539 [cond-mat.str-el]

DOI:

10.1016/j.aop.2020.168297

View in:

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Abstract: (Elsevier)

In this article we study field-theoretical aspects of multipolar topological insulators. Previous research has shown that such systems naturally couple to higher-rank tensor gauge fields that arise as a result of gauging dipole or subsystem U(1) symmetries. Here we propose a complementary framework using electric higher-form symmetries. We utilize the fact that gauging 1-form electric symmetries results in a 2-form gauge field which couples naturally to extended line-like objects: Wilson lines. In our context the Wilson lines are electric flux lines associated to the electric polarization of the system. This allows us to define a generalized 2-form Peierls’ substitution for dipoles that shows that the off-diagonal components of a rank-2 tensor gauge field Aij can arise as a lattice Peierls factor generated by the background antisymmetric 2-form gauge field. This framework has immediate applications: (i) it allows us to construct a manifestly topological quadrupolar response action given by a Dixmier–Douady invariant – a generalization of a Chern number for 2-form gauge fields – which makes plain the quantization of the quadrupole moment in the presence of certain crystal symmetries; (ii) it allows for a clearer interpretation of the rank-2 Berry phase calculation of the quadrupole moment; (iii) it allows for a proof of a generic Lieb–Schultz–Mattis theorem for dipole-conserving systems.

Note:

23+2 pages, 8 figures

Topological phases
Electric polarization
Interacting systems
Higher-form gauge fields
gauge field theory: tensor
symmetry: gauge
flux: electric
phase: topological
Wilson loop
dipole

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Figures(8)

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