  We study the impact of trimerization (breathing) of the nearest-neighbor (NN)
exchange on the planar XY spin-1/2 ferromagnet on the kagome lattice, including
additional four-site ring exchange. For uniform NN exchange, this model has
previously been shown to transit from a long-range ordered ferromagnet into a
Z2 quantum spin liquid by virtue of the ring exchange. Using quantum
Monte-Carlo calculations, based on the stochastic series expansion, we present
results for the spin stiffness, the quantum phase diagram, the longitudinal
static, as well as the transverse dynamic structure factor. Our results
corroborate 3D XY universality also at finite trimerization and suggest a
simple continuation of the quantum critical point of the uniform case into a
line in terms of rescaled exchange parameters. Moreover, at any trimerization
and in the ordered phase the elementary excitations can be understood very well
in terms of linear spin wave theory, while beyond the critical line, in the
spin liquid phase we find signatures of spinon continua.
