Multipole groups and fracton phenomena on arbitrary crystalline lattices

TL;DR

This paper systematically classifies multipole symmetries on arbitrary 2D crystal lattices, revealing new phenomena like emergent subsystem symmetries and vector charge conservation, expanding the understanding of fracton phases beyond hypercubic lattices.

Contribution

It provides a comprehensive classification method for multipole groups on arbitrary lattices and explores their physical implications, including novel symmetry phenomena.

Findings

Classification of multipole groups on all 2D Bravais lattices

Identification of emergent subsystem symmetry on triangular lattice

Discovery of exact multipolar symmetry with vector charge conservation

Abstract

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.