We analyze the zero temperature phase diagrams of the spin $S$ quantum antiferromagnet on square and triangular lattices with competing nearest and next-nearest exchange interactions as well as biquadratic couplings. We approach the problem from the large $S$ limit. Our primary focus is on determining the extent to which the existence and character of any quantum disordered phases can be inferred from this approach.

• Received 31 March 2020
• Accepted 21 May 2020

DOI:https://doi.org/10.1103/PhysRevB.101.214404