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
Sz=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
Sz=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.
Motivated by recent experiments on the vanadium oxyfluoride material DQVOF, we examine possible spin liquid phases on a breathing kagome lattice of
S=1/2 spins. By performing a projective symmetry group analysis, we determine the possible phases for both fermionic and bosonic
Z2 spin liquids on this lattice, and establish the correspondence between the two. The nature of the ground state of the Heisenberg model on the isotropic kagome lattice is a hotly debated topic, with both
Z2 and U(1) spin liquids argued to be plausible ground states. Using variational Monte Carlo techniques, we show that a gapped
Z2 spin liquid emerges as the clear ground state in the presence of this breathing anisotropy. Our results suggest that the breathing anisotropy helps to stabilize this spin liquid ground state, which may aid us in understanding the results of experiments and help to direct future numerical studies on these systems.
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.
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.
Here, the authors report the discovery of novel types of U(1) and \ensuremath{\mathbb{Z}}
2 quantum spin liquids on the pyrochlore lattice through a projective symmetry group classification. The classification highlights a special type of U(1) spin liquid, possessing an unusual symmetry-protected gapless multi-nodal-line structure in the spinon bands. The effect of gauge fluctuations for such a nodal structure is discussed. The leading contributions to the low-temperature specific heat are calculated, providing a clear experimental diagnostic of this U(1) spin liquid.
Pyrochlore magnets can be a unique platform to demonstrate numerous important concepts and applications of frustrated magnetic physics in modern condensed matter physics. Most works on pyrochlore magnets deal with the interacting spin-1/2 local moments, while much less works have studied the spin-1 systems. We here review the physics with interacting spin-1 local moments on the pyrochlore lattice to illustrate the potentially interesting physics associated with spin-1 magnets. The generic pyrochlore spin-1 model includes the antiferromagnetic Heisenberg interaction, the Dzyaloshinskii-Moriya interaction and the single-ion spin anisotropy. The global phase diagram of this generic spin model is reviewed, and the relation between different quantum phases in the phase diagram is clarified. The critical properties of the transition from the parent quantum paramagnet to the proximate orders are discussed. The presence of quantum order by disorder in the parts of the ordered phases is analyzed. The elementary excitations with respect to the ground states are further reviewed, and the topological natures of these excitations are carefully addressed. The materials’ relevance of the spin-1 pyrochlore magnets are finally reviewed. This review may provide insights about the interesting spin-1 local moments on frustrated systems.