Quantum-classical crossover in the spin-12 Heisenberg-Kitaev kagome magnet

The spin-1/2 Heisenberg kagome antiferromagnet is one of the paradigmatic playgrounds for frustrated quantum magnetism, with an extensive number of competing resonating valence bond (RVB) states emerging at low energies, including gapped and gapless spin liquids and valence bond crystals. Here we revisit the crossover from this quantum RVB phase to a semiclassical regime brought about by anisotropic Kitaev interactions, and focus on the precise mechanisms underpinning this crossover. To this end, we introduce a simple parametrization of the classical ground states (GSs) in terms of emergent Ising-like variables, and use this parametrization: (i) to construct an effective low-energy description of the order-by-disorder mechanism operating in a large part of the phase diagram and (ii) to contrast, side by side, exact diagonalization data obtained from the full basis with that obtained from the restricted (orthonormalized) basis of classical GSs. The results reveal that fluctuation corrections from states outside the restricted basis are strongly quenched inside the semiclassical regime (due to the large anisotropy spin gaps), and that the RVB phase survives up to a relatively large value of Kitaev anisotropy K. We further find that the pure Kitaev model admits a subextensive number of one-dimensional symmetries, which explains naturally the absence of classical and quantum order by disorder reported previously.