Broholm, C. et al. Quantum spin liquids. Science 367, eaay0668 (2020).
Savary, L. & Balents, L. Quantum spin liquids: a review. Rep. Prog. Phys. 80, 016502 (2016).
Anderson, P. W. Resonating valence bonds: a new kind of insulator?. Mater. Res. Bull. 8, 153 (1973).
Kitaev, A. Fault-tolerant quantum computation by anyons. Ann. Phys. 303, 2 (2003).
Anderson, P. W. The resonating valence bond state in La2CuO4 and superconductivity. Science 235, 1196 (1987).
Imajo, S. et al. Extraordinary π-electron superconductivity emerging from a quantum spin liquid. Phys. Rev. Res. 3, 033026 (2021).
Kivelson, S. A., Rokhsar, D. S. & Sethna, J. P. Topology of the resonating valence-bond state: solitons and high-Tc superconductivity. Phys. Rev. B 35, 8865 (1987).
Jiang, H.-C. & Kivelson, S. A. High temperature superconductivity in a lightly doped quantum spin liquid. Phys. Rev. Lett. 127, 097002 (2021).
Helton, J. S. et al. Spin dynamics of the spin-1/2 kagome lattice antiferromagnet ZnCu3(OH)6Cl2. Phys. Rev. Lett. 98, 107204 (2007).
Olariu, A. et al. 17O NMR study of the intrinsic magnetic susceptibility and spin dynamics of the quantum kagome antiferromagnet ZnCu3(OH)6Cl2. Phys. Rev. Lett. 100, 087202 (2008).
Han, T. H. et al. Fractionalized excitations in the spin-liquid state of a kagome-lattice antiferromagnet. Nature 492, 406 (2012).
Fu, M., Imai, T., Han, T.-H. & Lee, Y. S. Evidence for a gapped spin-liquid ground state in a kagome Heisenberg antiferromagnet. Science 350, 655 (2015).
Han, T.-H. et al. Correlated impurities and intrinsic spin-liquid physics in the kagome material herbertsmithite. Phys. Rev. B 94, 060409(R) (2016).
Wang, J. et al. Emergence of spin singlets with inhomogeneous gaps in the kagome lattice Heisenberg antiferromagnets Zn-barlowite and herbertsmithite. Nat. Phys. 17, 1109 (2021).
Khuntia, P. et al. Gapless ground state in the archetypal quantum kagome antiferromagnet ZnCu3(OH)6Cl2. Nat. Phys. 16, 469 (2020).
Jiang, H. C., Weng, Z. Y. & Sheng, D. N. Density matrix renormalization group numerical study of the kagome antiferromagnet. Phys. Rev. Lett. 101, 117203 (2008).
Yan, S., Huse, D. & White, S. Spin-liquid ground state of the s = 1/2 kagome Heisenberg antiferromagnet. Science 332, 1173 (2011).
Depenbrock, S., McCulloch, I. P. & Schollwöck, U. Nature of the spin-liquid ground state of the s = 1/2 Heisenberg model on the kagome lattice. Phys. Rev. Lett. 109, 067201 (2012).
Jiang, H. C., Wang, Z. & Balents, L. Identifying topological order by entanglement entropy. Nat. Phys. 8, 902 (2012).
Gong, S.-S., Zhu, W., Balents, L. & Sheng, D. N. Global phase diagram of competing ordered and quantum spin-liquid phases on the kagome lattice. Phys. Rev. B 91, 075112 (2015).
He, Y.-C., Zaletel, M. P., Oshikawa, M. & Pollmann, F. Signatures of dirac cones in a DMRG study of the kagome Heisenberg model. Phys. Rev. X 7, 031020 (2017).
Liao, H. J. et al. Gapless spin-liquid ground state in the s = 1/2 kagome antiferromagnet. Phys. Rev. Lett. 118, 137202 (2017).
Norman, M. R. Colloquium: herbertsmithite and the search for the quantum spin liquid. Rev. Mod. Phys. 88, 041002 (2016).
Han, T.-H., Singleton, J. & Schlueter, J. A. Barlowite: a spin-1/2 antiferromagnet with a geometrically perfect kagome motif. Phys. Rev. Lett. 113, 227203 (2014).
Feng, Z. et al. Gapped spin-1/2 spinon excitations in a new kagome quantum spin liquid compound Cu3Zn(OH)6FBr. Chinese Phys. Lett. 34, 077502 (2017).
Smaha, R. W. et al. Materializing rival ground states in the barlowite family of kagome magnets: quantum spin liquid, spin ordered, and valence bond crystal states. npj Quantum Mater. 5, 23 (2020).
Tustain, K. et al. From magnetic order to quantum disorder in the Zn-barlowite series of S = 1/2 kagomé antiferromagnets. npj Quantum Mater. 5, 74 (2020).
Wang, J. et al. Freezing of the lattice in the kagome lattice heisenberg antiferromagnet Zn-barlowite ZnCu3(OD)6FBr. Phys. Rev. Lett. 128, 157202 (2022).
Smaha, R. W. et al. High-energy spin excitations in the quantum spin liquid candidate Zn-substituted barlowite probed by resonant inelastic X-ray scattering. Phys. Rev. B 107, L060402 (2023).
Campello, A. C. et al. Phonon dynamics in quantum spin liquid and valence bond crystal states in the barlowite family of kagome magnets. Phys. Rev. B 111, 094406 (2025).
Freedman, D. E. et al. Site specific X-ray anomalous dispersion of the geometrically frustrated kagome magnet, herbertsmithite, ZnCu3(OH)6Cl2. J. Am. Chem. Soc. 132, 16185–16190 (2010).
Smaha, R. W. et al. Site-specific structure at multiple length scales in kagome quantum spin liquid candidates. Phys. Rev. Mater. 4, 124406 (2020).
Yuan, W. et al. Emergence of the spin polarized domains in the kagome lattice Heisenberg antiferromagnet Zn-barlowite (Zn0.95Cu0.05)Cu3(OD)6FBr. npj Quantum Mater. 7, 120 (2022).
Jeschke, H. O. et al. Barlowite as a canted antiferromagnet: theory and experiment. Phys. Rev. B 92, 094417 (2015).
Grohol, D. et al. Spin chirality on a two-dimensional frustrated lattice. Nat. Mater. 4, 323–328 (2005).
Han, T., Chu, S. & Lee, Y. S. Refining the spin Hamiltonian in the spin-\(\frac{1}{2}\) kagome lattice antiferromagnet ZnCu3(OH)6Cl2 using single crystals. Phys. Rev. Lett. 108, 157202 (2012).
Lee, P. A. & Nagaosa, N. Proposal to use neutron scattering to access scalar spin chirality fluctuations in kagome lattices. Phys. Rev. B 87, 064423 (2013).
Suttner, R., Platt, C., Reuther, J. & Thomale, R. Renormalization group analysis of competing quantum phases in the J1-J2 Heisenberg model on the kagome lattice. Phys. Rev. B 89, 020408 (2014).
Zorko, A. et al. Dzyaloshinsky-Moriya anisotropy in the spin-1/2 kagome compound ZnCu3(OH)6Cl2. Phys. Rev. Lett. 101, 026405 (2008).
Zhu, W., Shu Gong, S. & Sheng, D. N. Identifying spinon excitations from dynamic structure factor of spin-1/2 Heisenberg antiferromagnet on the kagome lattice. Proc. Natl Acad. Sci. USA 116, 5437 (2019).
Ferrari, F. et al. Static and dynamical signatures of Dzyaloshinskii-Moriya interactions in the Heisenberg model on the kagome lattice. SciPost Phys. 14, 139 (2023).
Punk, M., Chowdhury, D. & Sachdev, S. Topological excitations and the dynamic structure factor of spin liquids on the kagome lattice. Nat. Phys. 10, 289–293 (2014).
Feng, Z. et al. From claringbullite to a new spin liquid candidate Cu3Zn(OH)6FCl. Chinese Phys. Lett. 36, 017502 (2018).
Georgopoulou, M. et al. Magnetically ordered and kagome quantum spin liquid states in the Zn-doped claringbullite series. Phys. Rev. B 107, 024416 (2023).
Chatterjee, D. et al. From spin liquid to magnetic ordering in the anisotropic kagome Y-kapellasite Y3Cu9(OH)19Cl8: a single-crystal study. Phys. Rev. B 107, 125156 (2023).
Chen, X.-H., Huang, Y.-X., Pan, Y. & Mi, J.-X. Quantum spin liquid candidate YCu3(OH)6Br2[Brx(OH)1−x] (x ≈ 0.51): with an almost perfect kagome layer. J. Magn. Magn. Mater. 512, 167066 (2020).
Liu, J. et al. Gapless spin liquid behavior in a kagome Heisenberg antiferromagnet with randomly distributed hexagons of alternate bonds. Phys. Rev. B 105, 024418 (2022).
Zeng, Z. et al. Spectral evidence for dirac spinons in a kagome lattice antiferromagnet. Nat. Phys. 20, 1097 (2024).
White, S. R. Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett. 69, 2863 (1992).