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Multipole groups and fracton phenomena on arbitrary crystalline lattices

by Daniel Bulmash, Oliver Hart, Rahul Nandkishore

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Oliver Hart · Rahul Nandkishore
Submission information
Preprint Link: scipost_202308_00006v1  (pdf)
Date accepted: 2023-08-18
Date submitted: 2023-08-03 19:12
Submitted by: Hart, Oliver
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
  • Quantum Physics
Approach: Theoretical


Multipole symmetries are of interest in multiple contexts, from the study of fracton phases, to nonergodic quantum dynamics, to the exploration of new hydrodynamic universality classes. However, prior explorations have focused on continuum systems or hypercubic lattices. In this work, we systematically explore multipole symmetries on arbitrary crystal lattices. We explain how, given a crystal structure (specified by a space group and the occupied Wyckoff positions), one may systematically construct all consistent multipole groups. We focus on two-dimensional crystal structures for simplicity, although our methods are general and extend straightforwardly to three dimensions. We classify the possible multipole groups on all two-dimensional Bravais lattices, and on the kagome and breathing kagome crystal structures to illustrate the procedure on general crystal lattices. Using Wyckoff positions, we provide an in-principle classification of all possible multipole groups in any space group. We explain how, given a valid multipole group, one may construct an effective Hamiltonian and a low-energy field theory. We then explore the physical consequences, beginning by generalizing certain results originally obtained on hypercubic lattices to arbitrary crystal structures. Next, we identify two seemingly novel phenomena, including an emergent, robust subsystem symmetry on the triangular lattice, and an exact multipolar symmetry on the breathing kagome lattice that does not include conservation of charge (monopole), but instead conserves a vector charge. This makes clear that there is new physics to be found by exploring the consequences of multipolar symmetries on arbitrary lattices, and this work provides the map for the exploration thereof, as well as guiding the search for emergent multipolar symmetries and the attendant exotic phenomena in real materials based on nonhypercubic lattices.

Author comments upon resubmission

We would like to thank the referees for their time and their thoughtful reports, and we are pleased to hear their positive feedback on our manuscript.

We would like to resbumit our paper and reply to the referees. A list of changes to the manuscript can be found below. Thank you for your time and consideration.

Daniel Bulmash, Oliver Hart, and Rahul Nandkishore

List of changes

1) Updated some citations.
2) Added angles to Fig. 1 and updated caption accordingly.
3) Added a short explanation of how the "clouds" in Fig. 3 work at the end of Sec. II.B.3.
4) Added a disclaimer on notation overload just prior to Eq. (8).

Published as SciPost Phys. 15, 235 (2023)

Reports on this Submission

Anonymous Report 1 on 2023-8-3 (Invited Report)


The authors addressed all the questions and I certainly recommend the paper for publication in SciPost Physics.

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