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Quantum Monte Carlo (QMC) simulations are performed to study ground-stateproperties of a mixed spin-1 and spin-1/2 Lieb-lattice Heisenbergantiferromagnet, in order to get further insight beyond the modified spin-wave(MSW) study reported in [J. Phys. Soc. Jpn. 86, 014002 (2017)]. It is confirmedthat 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 spinreductions are inversely proportional to the sublattice sizes, is observed inour QMC simulation. We present a rigorous proof for spontaneous sublatticemagnetizations induced by an infinitesimal uniform magnetic field. Thecalculation process in the MSW theory is reexamined to clarify the mathematicalstructure behind the scaling relation for sublattice long-range orders.

Notes on Ground-State Properties of Mixed Spin-1 and Spin-1=2 Lieb-Lattice Heisenberg Antiferromagnets