Ergodicity breaking provably robust to arbitrary perturbations

Stephen, David T.; Hart, Oliver; Nandkishore, Rahul

doi:10.48550/arxiv.2209.03966

Cited by 2 publications

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“…[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%

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: Introductionmentioning

confidence: 96%

Multipole groups and fracton phenomena on arbitrary crystalline lattices

Bulmash,

Hart,

Nandkishore

2023

SciPost Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

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

mentioning

confidence: 99%

Multipole groups and fracton phenomena on arbitrary crystalline lattices

Bulmash¹,

Hart²,

Nandkishore³

2023

Preprint

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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 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. CONTENTS 3. Discussion D. Vector conserved quantities 1. Lattice Hamiltonian 2. Discussion V. Conclusions A. Group theory A.1. Irreducible representations of D 𝑀 A.2. Sorting polynomials into irreps A.3. Clebsch-Gordon coefficients for D 𝑀 B. Vector charge theory C. Discrete vs continuous translations D. From discrete derivatives to spin Hamiltonians D.1. Bravais lattice D.2. Introducing a basis D.3. Additional symmetries D.4. More general Hamiltonians E. Haar-random circuits and automaton dynamics References I. INTRODUCTIONMultipole symmetries have become a major topic of interest in condensed matter physics, quantum dynamics, and quantum information. This began with the work of Pretko [1] identifying conserved multipole moments as underlying the

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Ergodicity breaking provably robust to arbitrary perturbations

Cited by 2 publications

References 35 publications

Multipole groups and fracton phenomena on arbitrary crystalline lattices

Multipole groups and fracton phenomena on arbitrary crystalline lattices

Multipole groups and fracton phenomena on arbitrary crystalline lattices

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