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

TL;DR

This study uses Quantum Monte Carlo simulations to analyze the ground-state properties of a mixed spin-1 and spin-1/2 Lieb-lattice Heisenberg antiferromagnet, confirming and extending previous spin-wave theory results.

Contribution

It provides a validation of the modified spin-wave theory results through QMC simulations and offers a rigorous proof for sublattice magnetizations induced by infinitesimal magnetic fields.

Findings

QMC results agree with MSW predictions.

Sublattice spin reductions are inversely proportional to sublattice sizes.

Rigorous proof of spontaneous sublattice magnetizations.

Abstract

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.