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

TL;DR

This paper uses modified spin-wave theory with ordering vector optimization to analyze quantum antiferromagnets on anisotropic triangular and $J_1J_2J_3$ lattices, revealing quantum effects on magnetic order and potential non-magnetic phases.

Contribution

It introduces an advanced MSW approach with ordering vector optimization to accurately study quantum effects and phase transitions in complex magnetic models.

Findings

MSW correctly predicts quantum effects on magnetic ordering vectors.

Collinear order is favored over spiral order due to quantum effects.

Regions where MSW breaks down suggest possible non-magnetic ground states.

Abstract

We study the ground state phases of the $S=1/2$ Heisenberg quantum antiferromagnet on the spatially anisotropic triangular lattice and on the square 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 supplemented by ordering vector optimization. We compare the MSW results with exact diagonalization and projected-entangled-pair-states calculations, demonstrating their qualitative and quantitative reliability. We find that MSW theory correctly accounts for strong quantum effects on the ordering vector of the magnetic phases of the models under investigation: in particular collinear magnetic order is promoted at the expenses of non-collinear (spiral) order, and several spiral states which are stable at the classical level, disappear from the quantum phase diagram. Moreover, collinear states and non-collinear ones are never connected continuously, but they are separated by parameter regions in which MSW breaks down, signaling the possible appearance of a non-magnetic ground state. In the case of the spatially anisotropic triangular lattice, a large breakdown region appears also for weak couplings between the chains composing the lattice, suggesting the possible occurrence of a large non-magnetic region continuously connected with the spin-liquid state of the uncoupled chains.