arXiv:1902.10934 · Physical Review Letters

Rank–2 U ( 1 ) Spin Liquid on the Breathing Pyrochlore Lattice

Han Yan, Owen Benton, Ludovic D. C. Jaubert, Nic Shannon

Published Mar 26, 2020• 80 citations

Abstract

Higher-rank generalizations of electrodynamics have recently attracted considerable attention because of their ability to host "fracton" excitations, with connections to both fracton topological order and gravity. However, the search for higher-rank gauge theories in experiment has been greatly hindered by the lack of materially relevant microscopic models. Here we show how a spin liquid described by rank-2 U(1) gauge theory can arise in a magnet on the breathing pyrochlore lattice. We identify Yb-based breathing pyrochlores as candidate systems, and make explicit predictions for how the rank-2 U(1) spin liquid would manifest itself in experiment.

DOI: 10.1103/physrevlett.124.127203

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arXiv:1902.10934 · Physical Review Letters

Rank–2 U ( 1 ) Spin Liquid on the Breathing Pyrochlore Lattice

Han Yan, Owen Benton, Ludovic D. C. Jaubert, Nic Shannon

Published Mar 26, 2020• 80 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevlett.124.127203

Related papers

Dynamical signatures of rank-2 U(1) spin liquids

Emily Z. Zhang, Finn Lasse Buessen, Yong Baek Kim

Emergent $U(1)$ gauge theories and artificial photons in frustrated magnets are outstanding examples of many-body collective phenomena. The classical and quantum regimes of these systems provide platforms for classical and quantum spin liquids, and are the subject of current active theoretical and experimental investigations. Recently, realizations of rank-2 $U(1)$ (R2-U1) gauge theories in three-dimensional frustrated magnets have been proposed. Such systems in the quantum regime may lead to the so-called fracton ordered phases---a new class of topological order that has been associated with quantum stabilizer codes and holography. However, there exist few distinguishing characteristics of these states for their detection in real materials. Here we focus on the classical limit and present the dynamical spin structure factor for a R2-U1 spin liquid state on a breathing pyrochlore lattice. Remarkably, we find unique signatures of the R2-U1 state, and we contrast them with the results obtained from a more conventional $U(1)$ spin liquid. These results provide a path of investigation for future inelastic neutron scattering experiments on candidate materials.Emergent $U(1)$ gauge theories and artificial photons in frustrated magnets are outstanding examples of many-body collective phenomena. The classical and quantum regimes of these systems provide platforms for classical and quantum spin liquids, and are the subject of current active theoretical and experimental investigations. Recently, realizations of rank-2 $U(1)$ (R2-U1) gauge theories in three-dimensional frustrated magnets have been proposed. Such systems in the quantum regime may lead to the so-called fracton ordered phases---a new class of topological order that has been associated with quantum stabilizer codes and holography. However, there exist few distinguishing characteristics of these states for their detection in real materials. Here we focus on the classical limit and present the dynamical spin structure factor for a R2-U1 spin liquid state on a breathing pyrochlore lattice. Remarkably, we find unique signatures of the R2-U1 state, and we contrast them with the results obtained from a more conventional $U(1)$ spin liquid. These results provide a path of investigation for future inelastic neutron scattering experiments on candidate materials.

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arXiv:cond-mat/0305401Physical Review BFeb 12, 2004624 citations

Emergent

U(1)

gauge theories and artificial photons in frustrated magnets are outstanding examples of many-body collective phenomena. The classical and quantum regimes of these systems provide platforms for classical and quantum spin liquids, and are the subject of current active theoretical and experimental investigations. Recently, realizations of rank-2

U(1)

(R2-U1) gauge theories in three-dimensional frustrated magnets have been proposed. Such systems in the quantum regime may lead to the so-called fracton ordered phases---a new class of topological order that has been associated with quantum stabilizer codes and holography. However, there exist few distinguishing characteristics of these states for their detection in real materials. Here we focus on the classical limit and present the dynamical spin structure factor for a R2-U1 spin liquid state on a breathing pyrochlore lattice. Remarkably, we find unique signatures of the R2-U1 state, and we contrast them with the results obtained from a more conventional

U(1)

spin liquid. These results provide a path of investigation for future inelastic neutron scattering experiments on candidate materials.

Geometric frustration in spin systems offers potential routes to realize unusual phases of matter. The authors consider emergent quantum spin liquids of interacting

S=1/2

moments on the pyrochlore lattice with a breathing anisotropy, where two inequivalent sets of tetrahedra are present. They classify possible

{\mathbb{Z}}_{2}

and U(1) quantum spin liquids in this system and find a small number of physically motivated candidates. In particular, two degenerate U(1) spin liquids are identified for the antiferromagnetic Heisenberg model. The degeneracy is robust with respect to tuning the breathing anisotropy, but it can be lifted by a finite Dzyaloshinskii-Moriya interaction. The effect of gauge fluctuations in a gapless U(1) spin liquid is investigated for comparison with future experiments.

We study the

S=1/2

Heisenberg antiferromagnet on the pyrochlore lattice in the limit of strong easy-axis exchange anisotropy. We find, using only standard techniques of degenerate perturbation theory, that the model has a

U(1)

gauge symmetry generated by certain local rotations about the z axis in spin space. Upon addition of an extra local interaction in this and a related model with spins on a three-dimensional network of corner-sharing octahedra, we can write down the exact ground-state wave function with no further approximations. Using the properties of the soluble point we show that these models enter the

U(1)

spin liquid phase, a fractionalized spin liquid with an emergent

U(1)

gauge structure. This phase supports gapped

{S}^{z}=1/2

spinons carrying the

U(1)

``electric'' gauge charge, a gapped topological point defect or ``magnetic'' monopole, and a gapless ``photon,'' which in spin language is a gapless, linearly dispersing

{S}^{z}=0

collective mode. There are power-law spin correlations with a nontrivial angular dependence, as well as

U(1)

topological order. This state is stable to all zero-temperature perturbations and exists over a finite extent of the phase diagram. Using a convenient lattice version of electric-magnetic duality, we develop the effective description of the

U(1)

spin liquid and the adjacent soluble point in terms of Gaussian quantum electrodynamics and calculate a few of the universal properties. The resulting picture is confirmed by our numerical analysis of the soluble point wave function. Finally, we briefly discuss the prospects for understanding this physics in a wider range of models and for making contact with experiments.