  Inspired by the recent discovery of a new instability towards a chiral phase
of the classical Heisenberg model on the kagome lattice, we propose a specific
chiral spin liquid that reconciles different, well-established results
concerning both the classical and quantum models. This proposal is analyzed in
an extended mean-field Schwinger boson framework encompassing time reversal
symmetry breaking phases which allows both a classical and a quantum phase
description. At low temperatures, we find quantum fluctuations favor this
chiral phase, which is stable against small perturbations of second and third
neighbor interactions. For spin-1/2 this phase may be, beyond mean-field, a
chiral gapped spin liquid. Such a phase is consistent with Density Matrix
Renormalization Group results of Yan et al. (Science 322, 1173 (2011)).
Mysterious features of the low lying excitations of exact diagonalization
spectra also find an explanation in this framework. Moreover, thermal
fluctuations compete with quantum ones and induce a transition from this flux
phase to a planar zero flux phase at a non zero value of the renormalized
temperature (T/S^2), reconciling these results with those obtained for the
classical system.
