Anomalous hydrodynamics with triangular point group in 2 + 1 dimensions

Qi, Marvin; Guo, Jinkang; Lucas, Andrew

doi:10.48550/arxiv.2209.08108

Cited by 2 publications

(3 citation statements)

References 42 publications

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“…As an aside, we further note that if K ′ ̸ = 0, then consistency with the second law of thermodynamics then requires that K ̸ = 0 in (3.21) [34]. More recently, it was shown that the existence of such a K ′ term will require an exotic kind of chiral anomaly [42], which can be found in actual lattice models (but is unlikely to exist in electron fluids).…”

Section: Continuity Equations and Constitutive Relationsmentioning

confidence: 85%

Hydrodynamics with triangular point group

2023

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When continuous rotational invariance of a two-dimensional fluid is broken to the discrete, dihedral subgroup D_6D6 - the point group of an equilateral triangle - the resulting anisotropic hydrodynamics breaks both spatial-inversion and time-reversal symmetries, while preserving their combination. In this work, we present the hydrodynamics of such D_6D6-symmetric fluids, identifying new symmetry-allowed dissipative terms in the hydrodynamic equations of motion. We propose two experiments - both involving high-purity solid-state materials with D_6D6-invariant Fermi surfaces - that are sensitive to these new coefficients in a D_6D6-invariant electron fluid. In particular, we propose a local current imaging experiment (which is present-day realizable with nitrogen vacancy center magnetometry) in a hexagonal device, whose D_6D6-exploiting boundary conditions enable the unambiguous detection of these novel transport coefficients.

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Section: Continuity Equations and Constitutive Relationsmentioning

confidence: 85%

Hydrodynamics with triangular point group

2023

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“…More generally, the first-order derivatives will annihilate all functions spanned by 𝑔(𝑧) = 𝑧 𝑛 and 𝑔(𝑧) = 𝑖𝑧 𝑛 for 𝑛 ∈ N 0 . Such holomorphic conserved charges also arise in the context of hydrodynamics in the presence of a triangular point group when the current tensor transforms in the vector representation of D 3 [52].…”

Section: Vector Conserved Quantitiesmentioning

confidence: 99%

“…If we had not included 𝑓 (x) = 𝑦 3 − 3𝑥 2 𝑦 in M, we would additionally be able to introduce a second third-order derivative, D 2 = 𝜕 3 𝑦 − 3𝜕 2 𝑥 𝜕 𝑦 . We note in passing that the operator D 1 also naturally appears in the context of hydrodynamics in the presence of the point group D 3 , since it may be written compactly as D 1 = 𝜆 𝑖 𝑗 𝑘 𝜕 𝑖 𝜕 𝑗 𝜕 𝑘 , with 𝜆 𝑖 𝑗 𝑘 the third-order D 3 -invariant tensor [52,53].…”

Section: Subsystem Symmetries In 2d From 𝑶 (1) Symmetriesmentioning

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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Anomalous hydrodynamics with triangular point group in 2 + 1 dimensions

Cited by 2 publications

References 42 publications

Hydrodynamics with triangular point group

Hydrodynamics with triangular point group

Multipole groups and fracton phenomena on arbitrary crystalline lattices

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