25 research outputs found
Multipole groups and fracton phenomena on arbitrary crystalline lattices
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.Comment: 23 pages, 9 figure