  Quantum Monte Carlo (QMC) simulations are performed to study ground-state
properties of a mixed spin-1 and spin-1/2 Lieb-lattice Heisenberg
antiferromagnet, in order to get further insight beyond the modified spin-wave
(MSW) study reported in [J. Phys. Soc. Jpn. 86, 014002 (2017)]. It is confirmed
that the MSW results are in good agreement with the QMC results. In particular,
the scaling relation found in the MSW study, which argues that sublattice spin
reductions are inversely proportional to the sublattice sizes, is observed in
our QMC simulation. We present a rigorous proof for spontaneous sublattice
magnetizations induced by an infinitesimal uniform magnetic field. The
calculation process in the MSW theory is reexamined to clarify the mathematical
structure behind the scaling relation for sublattice long-range orders.
