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The spin ice materials, including Ho2Ti2O7 and Dy2Ti2O7, are rare earth pyrochlore magnets which, at low temperatures, enter a constrained paramagnetic state with an emergent gauge freedom. Remarkably, the spin ices provide one of very few experimentally realised examples of fractionalization because their elementary excitations can be regarded as magnetic monopoles and, over some temperature range, the spin ice materials are best described as liquids of these emergent charges. In the presence of quantum fluctuations, one can obtain, in principle, a quantum spin liquid descended from the classical spin ice state characterised by emergent photon-like excitations. Whereas in classical spin ices the excitations are akin to electrostatic charges, in the quantum spin liquid these charges interact through a dynamic and emergent electromagnetic field. In this review, we describe the latest developments in the study of such a quantum spin ice, focussing on the spin liquid phenomenology and the kinds of materials where such a phase might be found.
We use numerical linked cluster (NLC) expansions to compute the specific heat, C(T), and entropy, S(T), of a quantum spin ice model of Yb2Ti2O7 using anisotropic exchange interactions recently determined from inelastic neutron scattering measurements
Motivated by the recent synthesis of the spin-1 A-site spinel NiRh$_{text 2}$O$_{text 4}$, we investigate the classical to quantum crossover of a frustrated $J_1$-$J_2$ Heisenberg model on the diamond lattice upon varying the spin length $S$. Applyin
The Coulombic quantum spin liquid in quantum spin ice is an exotic quantum phase of matter that emerges on the pyrochlore lattice and is currently actively searched for. Motivated by recent experiments on the Yb-based breathing pyrochlore material Ba
We study gapless quantum spin chains with spin 1/2 and 1: the Fredkin and Motzkin models. Their entangled groundstates are known exactly but not their excitation spectra. We first express the groundstates in the continuum which allows for the calcula
We show that gapless spin liquids, which are potential candidates to describe the ground state of frustrated Heisenberg models in two dimensions, become trivial insulators on cylindrical geometries with an even number of legs. In particular, we repor