Exact solution for the filling-induced thermalization transition in a one-dimensional fracton system

Pozderac, Calvin; Speck, Steven; Feng, Xiaozhou; Huse, David A.; Skinner, B. F.

doi:10.1103/physrevb.107.045137

Cited by 14 publications

(2 citation statements)

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“…as the unique solution. The polynomial y 3 − 3x 2 y can also be included in the multipole group (31) without changing the fundamental solution (32). If y 3 − 3x 2 y is instead the only third-order polynomial in the multipole group, then the allowed gates are no longer unique; the same two solutions are permitted as for the set of multipole moments in Eq.…”

Section: Triangular Latticementioning

confidence: 99%

“…[12] that imposing multipolar symmetries on quantum dynamics could give rise to ergodicity breaking. This was later explained in terms of Hilbert space shattering/fragmentation [13][14][15], a phenomenon that has been observed experimentally [16,17], which could be harnessed for both quantum memories [13] and metrology [18], and which has been undergoing intensive exploration [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. In a third development, it was realized in Refs.…”

Section: Introductionmentioning

confidence: 96%

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Multipole groups and fracton phenomena on arbitrary crystalline lattices

Bulmash,

Hart,

Nandkishore

2023

SciPost Phys.

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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 a consistent lattice 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 apparently novel phenomena: 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.

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Section: Triangular Latticementioning

confidence: 99%