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Spin-1/2 kagome antiferromagnet (AFM) is one of the most studied models infrustrated magnetism since it is a promising candidate to host exotic spinliquid states. However, despite numerous studies using both analytical andnumerical approaches, the nature of the ground state and low-energy excitationsin this system remain elusive. This is related to the difficulty in determiningthe spin gap in various calculations. We present the results of ourinvestigation of the Kagome AFM using the recently developed group equivariantconvolutional neural networks - an advanced machine learning technique forstudying strongly frustrated models. The approach, combined with variationalMonte Carlo, introduces significant improvement of the achievable resultsaccuracy in comparison with approaches based on other neural networkarchitectures that lack generalization quality for frustrated spin systems.Contrary to the results obtained previously with various methods, thatpredicted Z_2 or U(1) Dirac spin liquid states, our results strongly indicatethat the ground state of the kagome lattice antiferromagnet is a spinon pairdensity wave that does not break time-reversal symmetry or any of the latticesymmetries. The found state appears due to the spinon Cooper pairinginstability close to two Dirac points in the spinon energy spectrum andresembles the pair density wave state studied previously in the context ofunderdoped cuprate superconductors in connection with the pseudogap phase. Thestate has significantly lower energy than the lowest energy states found by theSU(2) symmetric density matrix renormalization group calculations and othermethods.

Spin-1/2 kagome Heisenberg antiferromagnet: Machine learning discovery of the spinon pair density wave ground state