We thank P. Ginsparg, J. Hoffman, S. Kivelson, R. Melko, A. Millis, M. Stoudenmire, K. Weinberger and J. Zaanen for discussions and communications. A.M. and Y.Z. acknowledge support from DOE DE-SC0010313; Y.Z. acknowledges support from DOE DE-SC0018946; E.-A.K. and J.C.S.D. acknowledge support by the Cornell Center for Materials Research with funding from the NSF MRSEC programme (DMR-1719875); E.K. and K.C. acknowledge support from the NSF through grant number DMR-1609560. E.-A.K. and E.K. acknowledge support from the Kavli Institute for Theoretical Physics (where initial discussions about the project took place), which is supported in part by the NSF under grant number PHY-1748958. S.U. and H.E. acknowledge support from a Grant-in-aid for Scientific Research from the Ministry of Science and Education of Japan and the Global Centers of Excellence Program of the Japan Society for the Promotion of Science. K.F. and J.C.S.D. acknowledge support from the US Department of Energy, Office of Basic Energy Sciences, under contract number DEAC02-98CH10886; S.D.E, M.H.H. and J.C.S.D. acknowledge support from the Moore Foundation’s EPiQS Initiative through grant GBMF4544; J.C.S.D. acknowledges support from Science Foundation Ireland under award SFI 17/RP/5445 and from the European Research Council (ERC) under award number DLV-788932.

Reviewer information

Nature thanks Giuseppe Carleo, Andrea Perali and the other anonymous reviewer(s) for their contribution to the peer review of this work.