Order-parameter fluctuations in the frustrated Heisenberg model on the square lattice

The $T=0$ dynamics of the two-dimensional $s=1/2$ Heisenberg model with competing nearest-neighbor $(J_1)$ and next-nearest-neighbor $(J_2)$ interactions is explored via the recursion method, specifically the frequency-dependent fluctuations of the order parameters associated with some of the known or suspected ordering tendencies in this system, i.e. N\'eel, collinear, dimer, and chiral order. The results for the dynamic structure factors of the respective fluctuation operators show a strong indication of collinear order at $J_2/J_1 \gtrsim 0.6$ and a potential for dimer order at $0.5 \lesssim J_2/J_1 \lesssim 0.6$, whereas the chiral ordering tendency is observed to be considerably weaker.