Gardner, J. S., Gingras, M. J. P. & Greedan, J. E. Magnetic pyrochlore oxides. Rev. Mod. Phys. 82, 53–107 (2010).
Savary, L. & Balents, L. Quantum spin liquids: a review. Rep. Prog. Phys. 80, 016502 (2017).
Zhou, Y., Kanoda, K. & Ng, T.-K. Quantum spin liquid states. Rev. Mod. Phys. 89, 025003 (2017).
Hallas, A. M., Gaudet, J. & Gaulin, B. D. in Annual Review of Condensed Matter Physics Vol. 9 (eds Sachdev, S. & Marchetti, M. C.) 105–124 (Annual Reviews, 2018).
Broholm, C. et al. Quantum spin liquids. Science 367, eaay0668 (2020).
Anderson, P. W. Resonating valence bonds: a new kind of insulator? Mater. Res. Bull. 8, 153–160 (1973).
Anderson, P. W. The resonating valence bond state in La2CuO4 and superconductivity. Science 235, 1196–1198 (1987).
Lee, P. A., Nagaosa, N. & Wen, X. G. Doping a Mott insulator: physics of high-temperature superconductivity. Rev. Mod. Phys. 78, 17–85 (2006).
Kitaev, A. Y. Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2–30 (2003).
Kitaev, A. Anyons in an exactly solved model and beyond. Ann. Phys. 321, 2–111 (2006).
Takagi, H., Takayama, T., Jackeli, G., Khaliullin, G. & Nagler, S. E. Concept and realization of Kitaev quantum spin liquids. Nat. Rev. Phys. 1, 264–280 (2019).
Han, T. H. et al. Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet. Nature 492, 406–410 (2012).
Norman, M. R. Colloquium: herbertsmithite and the search for the quantum spin liquid. Rev. Mod. Phys. 88, 041002 (2016).
Shen, Y. et al. Evidence for a spinon Fermi surface in a triangular-lattice quantum-spin-liquid candidate. Nature 540, 559–562 (2016).
Paddison, J. A. M. et al. Continuous excitations of the triangular-lattice quantum spin liquid YbMgGaO4. Nat. Phys. 13, 117–122 (2016).
Dai, P.-L. et al. Spinon Fermi surface spin liquid in a triangular lattice antiferromagnet NaYbSe2. Phys. Rev. 11, 021044 (2021).
Balz, C. et al. Physical realization of a quantum spin liquid based on a complex frustration mechanism. Nat. Phys. 12, 942–947 (2016).
Scheie, A. O. et al. Proximate spin liquid and fractionalization in the triangular antiferromagnet KYbSe2.Nat. Phys. 20, 74–79 (2024).
Xie, T. et al. Complete field-induced spectral response of the spin-1/2 triangular-lattice antiferromagnet CsYbSe2. npj Quantum Mater. 8, 48 (2023).
Scheie, A. et al. Witnessing entanglement in quantum magnets using neutron scattering. Phys. Rev. B 103, 224434 (2021).
Sherman, N. E., Dupont, M. & Moore, J. E. Spectral function of the J1–J2 Heisenberg model on the triangular lattice. Phys. Rev. B 107, 165146 (2023).
Bramwell, S. T. & Gingras, M. J. P. Spin ice state in frustrated magnetic pyrochlore materials. Science 294, 1495–1501 (2001).
Bramwell, S. T. & Harris, M. J. The history of spin ice. J. Phys. Condens. Matter 32, 374010 (2020).
Fennell, T. et al. Magnetic Coulomb phase in the spin ice Ho2Ti2O7. Science 326, 415–417 (2009).
Gingras, M. J. P. & McClarty, P. A. Quantum spin ice: a search for gapless quantum spin liquids in pyrochlore magnets. Rep. Prog. Phys. 77, 056501 (2014).
Hermele, M., Fisher, M. P. A. & Balents, L. Pyrochlore photons: the U(1) spin liquid in a S = 1/2 three-dimensional frustrated magnet. Phys. Rev. B 69, 064404 (2004).
Banerjee, A., Isakov, S. V., Damle, K. & Kim, Y. B. Unusual liquid state of hard-core bosons on the pyrochlore lattice. Phys. Rev. Lett. 100, 047208 (2008).
Huang, C.-J., Deng, Y., Wan, Y. & Meng, Z. Y. Dynamics of topological excitations in a model quantum spin ice. Phys. Rev. Lett. 120, 167202 (2018).
Kato, Y. & Onoda, S. Numerical evidence of quantum melting of spin ice: quantum-to-classical crossover. Phys. Rev. Lett. 115, 077202 (2015).
Benton, O., Sikora, O. & Shannon, N. Seeing the light: experimental signatures of emergent electromagnetism in a quantum spin ice. Phys. Rev. B 86, 075154 (2012).
Shannon, N., Sikora, O., Pollmann, F., Penc, K. & Fulde, P. Quantum ice: a quantum Monte Carlo study. Phys. Rev. Lett. 108, 067204 (2012).
Pace, S. D., Morampudi, S. C., Moessner, R. & Laumann, C. R. Emergent fine structure constant of quantum spin ice is large. Phys. Rev. Lett. 127, 117205 (2021).
Savary, L. & Balents, L. Coulombic quantum liquids in spin-1/2 pyrochlores. Phys. Rev. Lett. 108, 037202 (2012).
Ross, K. A., Savary, L., Gaulin, B. D. & Balents, L. Quantum excitations in quantum spin ice. Phys. Rev. 1, 021002 (2011).
Thompson, J. D. et al. Quasiparticle breakdown and spin Hamiltonian of the frustrated quantum pyrochlore Yb2Ti2O7 in a magnetic field. Phys. Rev. Lett. 119, 057203 (2017).
Sibille, R. et al. Experimental signatures of emergent quantum electrodynamics in Pr2Hf2O7. Nat. Phys. 14, 711–715 (2018).
Scheie, A. et al. Multiphase magnetism in Yb2Ti2O7. Proc. Natl Acad. Sci. USA 117, 27245–27254 (2020).
Gaudet, J. et al. Quantum spin ice dynamics in the dipole-octupole pyrochlore magnet Ce2Zr2O7. Phys. Rev. Lett. 122, 187201 (2019).
Gao, B. et al. Experimental signatures of a three-dimensional quantum spin liquid in effective spin-1/2 Ce2Zr2O7 pyrochlore. Nat. Phys. 15, 1052–1057 (2019).
Sibille, R. et al. Candidate quantum spin liquid in the Ce3+ pyrochlore stannate Ce2Sn2O7. Phys. Rev. Lett. 115, 097202 (2015).
Sibille, R. et al. A quantum liquid of magnetic octupoles on the pyrochlore lattice. Nat. Phys. 16, 546–552 (2020).
Smith, E. M. et al. The case for a U(1) quantum spin liquid ground state in the dipole-octupole pyrochlore Ce2Zr2O7. Phys. Rev. X 12, 021015 (2022).
Porée, V. et al. Crystal-field states and defect levels in candidate quantum spin ice Ce2Hf2O7. Phys. Rev. Mater. 6, 044406 (2022).
Porée, V. et al. Dipolar-octupolar correlations and hierarchy of exchange interactions in Ce2Hf2O7. Preprint at https://arxiv.org/abs/2305.08261 (2023).
Yahne, D. R. et al. Dipolar spin ice regime proximate to an all-in-all-out Néel ground state in the dipolar-octupolar pyrochlore Ce2Sn2O7. Phys. Rev. X 14, 011005 (2024).
Huang, Y.-P., Chen, G. & Hermele, M. Quantum spin ices and topological phases from dipolar-octupolar doublets on the pyrochlore lattice. Phys. Rev. Lett. 112, 167203 (2014).
Li, Y.-D. & Chen, G. Symmetry enriched U(1) topological orders for dipole-octupole doublets on a pyrochlore lattice. Phys. Rev. B 95, 041106 (2017).
Benton, O. Ground-state phase diagram of dipolar-octupolar pyrochlores. Phys. Rev. B 102, 104408 (2020).
Bhardwaj, A. et al. Sleuthing out exotic quantum spin liquidity in the pyrochlore magnet Ce2Zr2O7. npj Quantum Mater. 7, 51 (2022).
Hosoi, M., Zhang, E. Z., Patri, A. S. & Kim, Y. B. Uncovering footprints of dipolar-octupolar quantum spin ice from neutron scattering signatures. Phys. Rev. Lett. 129, 097202 (2022).
Desrochers, F., Chern, L. E. & Kim, Y. B. Symmetry fractionalization in the gauge mean-field theory of quantum spin ice. Phys. Rev. B 107, 064404 (2023).
Desrochers, F. & Kim, Y. B. Spectroscopic signatures of fractionalization in octupolar quantum spin ice. Phys. Rev. Lett. 132, 066502 (2024).
Gao, B. et al. Magnetic field effects in an octupolar quantum spin liquid candidate. Phys. Rev. B 106, 094425 (2022).
Smith, E. M. et al. Quantum spin ice response to a magnetic field in the dipole-octupole pyrochlore Ce2Zr2O7. Phys. Rev. B 108, 054438 (2023).
Beare, J. et al. µSR study of the dipole-octupole quantum spin ice candidate Ce2Zr2O7. Phys. Rev. B 108, 174411 (2023).
Porée, V. et al. Evidence for fractional matter coupled to an emergent gauge field in a quantum spin ice. Nat. Phys. 21, 83–88 (2024).
Moon, R. M., Riste, T. & Koehler, W. C. Polarization analysis of thermal-neutron scattering. Phys. Rev. 181, 920–931 (1969).
Liu, P. et al. In-plane uniaxial pressure-induced out-of-plane antiferromagnetic moment and critical fluctuations in BaFe2As2. Nat. Commun. 11, 5728 (2020).
Dai, P. Antiferromagnetic order and spin dynamics in iron-based superconductors. Rev. Mod. Phys. 87, 855–896 (2015).
Lee, S., Onoda, S. & Balents, L. Generic quantum spin ice. Phys. Rev. B 86, 104412 (2012).
Chen, G. Spectral periodicity of the spinon continuum in quantum spin ice. Phys. Rev. B 96, 085136 (2017).
Yao, X.-P., Li, Y.-D. & Chen, G. Pyrochlore U(1) spin liquid of mixed-symmetry enrichments in magnetic fields. Phys. Rev. Res. 2, 013334 (2020).
Patri, A. S., Hosoi, M. & Kim, Y. B. Distinguishing dipolar and octupolar quantum spin ices using contrasting magnetostriction signatures. Phys. Rev. Res. 2, 023253 (2020).
Wen, J. J. et al. Disordered route to the Coulomb quantum spin liquid: random transverse fields on spin ice in Pr2Zr2O7. Phys. Rev. Lett. 118, 107206 (2017).
Kofu, M. et al. Magnetic boson peak in classical spin glasses. Phys. Rev. Res. 6, 013006 (2024).
Matsumoto, Y. & Nakatsuji, S. Relaxation calorimetry at very low temperatures for systems with internal relaxation. Rev. Sci. Instrum. 89, 033908 (2018).
Popa, K. et al. A re-evaluation of the heat capacity of cerium zirconate Ce2Zr2O7. J. Phys. Chem. Solids 69, 70–75 (2008).
Lan, G., Ouyang, B. & Song, J. The role of low-lying optical phonons in lattice thermal conductance of rare-earth pyrochlores: a first-principle study. Acta Mater. 91, 304–317 (2015).
Anderson, P. W., Halperin, B. I. & Varma, C. M. Anomalous low-temperature thermal properties of glasses and spin glasses. Philos. Mag.-J. Theor. Exp. Appl. Phys. 25, 1–9 (1972).
Binder, K. & Young, A. P. Spin glasses: experimental facts, theoretical concepts, and open questions. Rev. Mod. Phys. 58, 801–976 (1986).
Ramirez, A. P., Espinosa, G. P. & Cooper, A. S. Strong frustration and dilution-enhanced order in a quasi-2D spin glass. Phys. Rev. Lett. 64, 2070–2073 (1990).
Nakatsuji, S. et al. Spin disorder on a triangular lattice. Science 309, 1697–1700 (2005).