- Karim Essafi: Okinawa Inst Sci &Technol, Onna, Okinawa 904 0495, Japan. ORCID
- Owen Benton: Okinawa Inst Sci &Technol, Onna, Okinawa 904 0495, Japan.
- L D C Jaubert: Okinawa Inst Sci &Technol, Onna, Okinawa 904 0495, Japan.
Despite its deceptive simplicity, few concepts have more fundamental implications than chirality, from the therapeutic activity of drugs to the fundamental forces of nature. In magnetic materials, chirality gives rise to unconventional phenomena such as the anomalous Hall effect and multiferroicity, taking an enhanced flavour in the so-called spin-liquid phases where magnetic disorder prevails. Kagome systems sit at the crossroad of these ideas. Motivated by the recent synthesis of rare-earth kagome materials and the progresses in optical-lattice experiments, we bring together an entire network of spin liquids with anisotropic and Dzyaloshinskii-Moriya interactions. This network revolves around the Ising antiferromagnet and ends on (ferromagnetic) chiral spin liquids with spontaneously broken time-reversal symmetry. As for the celebrated Heisenberg antiferromagnet, it now belongs to a triad of equivalently disordered phases. The present work provides a unifying theory of kagome spin liquids with time-reversal invariant nearest-neighbour Hamiltonians.