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We study the ground state phases of the $S=1/2$ Heisenberg quantumantiferromagnet on the spatially anisotropic triangular lattice and on thesquare lattice with up to next-next-nearest neighbor coupling (the $J_1J_2J_3$model), making use of Takahashi's modified spin-wave (MSW) theory supplementedby ordering vector optimization. We compare the MSW results with exactdiagonalization and projected-entangled-pair-states calculations, demonstratingtheir qualitative and quantitative reliability. We find that MSW theorycorrectly accounts for strong quantum effects on the ordering vector of themagnetic phases of the models under investigation: in particular collinearmagnetic order is promoted at the expenses of non-collinear (spiral) order, andseveral spiral states which are stable at the classical level, disappear fromthe quantum phase diagram. Moreover, collinear states and non-collinear onesare never connected continuously, but they are separated by parameter regionsin which MSW breaks down, signaling the possible appearance of a non-magneticground state. In the case of the spatially anisotropic triangular lattice, alarge breakdown region appears also for weak couplings between the chainscomposing the lattice, suggesting the possible occurrence of a largenon-magnetic region continuously connected with the spin-liquid state of theuncoupled chains.

new journal of physics

Modified spin-wave theory with ordering vector optimization II:  Spatially anisotropic triangular lattice and $J_1J_2J_3$ model with  Heisenberg interactions