  Spin-1/2 kagome antiferromagnet (AFM) is one of the most studied models in
frustrated magnetism since it is a promising candidate to host exotic spin
liquid states. However, despite numerous studies using both analytical and
numerical approaches, the nature of the ground state and low-energy excitations
in this system remain elusive. This is related to the difficulty in determining
the spin gap in various calculations. We present the results of our
investigation of the Kagome AFM using the recently developed group equivariant
convolutional neural networks - an advanced machine learning technique for
studying strongly frustrated models. The approach, combined with variational
Monte Carlo, introduces significant improvement of the achievable results
accuracy in comparison with approaches based on other neural network
architectures that lack generalization quality for frustrated spin systems.
Contrary to the results obtained previously with various methods, that
predicted Z_2 or U(1) Dirac spin liquid states, our results strongly indicate
that the ground state of the kagome lattice antiferromagnet is a spinon pair
density wave that does not break time-reversal symmetry or any of the lattice
symmetries. The found state appears due to the spinon Cooper pairing
instability close to two Dirac points in the spinon energy spectrum and
resembles the pair density wave state studied previously in the context of
underdoped cuprate superconductors in connection with the pseudogap phase. The
state has significantly lower energy than the lowest energy states found by the
SU(2) symmetric density matrix renormalization group calculations and other
methods.
