Quantum spin liquids may be considered 'quantum disordered' ground states of spin systems, in which zero-point fluctuations are so strong that they prevent conventional magnetic long-range order. More interestingly, quantum spin liquids are prototypical examples of ground states with massive many-body entanglement, which is of a degree sufficient to render these states distinct phases of matter. Their highly entangled nature imbues quantum spin liquids with unique physical aspects, such as non-local excitations, topological properties, and more. In this review, we discuss the nature of such phases and their properties based on paradigmatic models and general arguments, and introduce theoretical technology such as gauge theory and partons, which are conveniently used in the study of quantum spin liquids. An overview is given of the different types of quantum spin liquids and the models and theories used to describe them. We also provide a guide to the current status of experiments in relation to study quantum spin liquids, and to the diverse probes used therein.

Recent work has highlighted remarkable effects of classical thermal fluctuations in the dipolar spin ice compounds, such as ''artificial magnetostatics,'' manifesting as Coulombic power-law spin correlations and particles behaving as diffusive ''magnetic monopoles.'' In this paper, we address quantum spin ice, giving a unifying framework for the study of magnetism of a large class of magnetic compounds with the pyrochlore structure, and, in particular, discuss Rare-earth pyrochlores display a diverse set of fascinating physical phenomena [1]. One of the most interesting aspects of these materials from the point of view of fundamental physics is the strong frustration experienced by coupled magnetic moments on this lattice. The best explored materials exhibiting this frustration are the ''spin ice'' compounds, Ho 2 Ti 2 O 7 , Dy 2 Ti 2 O 7 , in which the moments can be regarded as classical spins with a strong easyaxis (Ising) anisotropy [2,3]. The frustration of these moments results in a remarkable classical spin liquid regime displaying Coulombic correlations and emergent ''magnetic monopole'' excitations that have now been studied extensively in theory and experiment [4][5][6].Strong quantum effects are absent in the spin ice compounds, but can be significant in other rare-earth pyrochlores. In particular, in many materials the low-energy spin dynamics may be reduced to that of an effective spin S ¼ 1=2 moment, with the strongest possible quantum effects expected. In this case symmetry considerations reduce the exchange constant phase space of the nearestneighbor exchange Hamiltonian to a maximum of three dimensionless parameters [7] [9,10]. This makes these materials beautiful examples of highly frustrated and strongly quantum magnets on the pyrochlore lattice. They are also nearly ideal subjects for detailed experimental investigation, existing as they do in large high-purity single crystals, and with large magnetic moments amenable to neutron scattering studies. Yb 2 Ti 2 O 7 is particularly appealing because its lowest Kramers doublet is extremely well separated from the first excited one [11], and a very large single-crystal neutron scattering data set is available, allowing us to determine the full Hamiltonian quantitatively, as we will show. Although we specialize to Yb 2 Ti 2 O 7 in the present article, the theoretical considerations and parameter determination method described here will very generally apply to all pyrochlore materials where exchange interactions dominate, and whose dynamics can be described by that of a single doublet.Theoretical studies have pointed to the likelihood of unusual ground states of quantum antiferromagnets on the pyrochlore lattice [12,13]. Most exciting is the possibility of a quantum spin liquid (QSL) state, which avoids magnetic ordering and freezing even at absolute zero temperature, and whose elementary excitations carry fractional quantum numbers and are decidedly different from spin waves [14]. Although one neutron study [15] supported ferromagnetic order in Yb 2...

We develop a nonperturbative gauge mean field theory (gMFT) method to study a general effective spin-1/2 model for magnetism in rare earth pyrochlores. gMFT is based on a novel exact slave-particle formulation, and matches both the perturbative regime near the classical spin ice limit and the semiclassical approximation far from it. We show that the full phase diagram contains two exotic phases: a quantum spin liquid and a Coulombic ferromagnet, both of which support deconfined spinon excitations and emergent quantum electrodynamics. Phenomenological properties of these phases are discussed.

Here we establish the systematic existence of a U(1) degeneracy of all symmetry-allowed Hamiltonians quadratic in the spins on the pyrochlore lattice, at the mean-field level. By extracting the Hamiltonian of Er(2)Ti(2)O(7) from inelastic neutron scattering measurements, we then show that the U(1)-degenerate states of Er(2)Ti(2)O(7) are its classical ground states, and unambiguously show that quantum fluctuations break the degeneracy in a way which is confirmed by experiment. The degree of symmetry protection of the classical U(1) degeneracy in Er(2)Ti(2)O(7) is unprecedented in other materials. As a consequence, our observation of order by disorder is unusually definitive. We provide further verifiable consequences of this phenomenon, and several additional comparisons between theory and experiment.