Quantum melting of long-range ordered quantum antiferromagnets investigated by momentum-space continuous similarity transformations

We apply continuous similarity transformations (CSTs) to study the zero-temperature breakdown of long-range ordered quantum antiferromagnets. The CST flow equations are truncated in momentum space by the scaling dimension so that all operators with scaling dimension up to two are taken into account. We determine the quantum phase transition out of the N\'eel-ordered phase in the unfrustrated square lattice Heisenberg bilayer as well as the quantum melting of the N\'eel-ordered and columnar phase in the highly frustrated $J_1$-$J_2$ model on the square lattice. In all cases the CST is set up to isolate the ground state so that the stability of the flow equations, the ground-state energy, and the sublattice magnetization are used to explore the long-range ordered phases. We extract quantum-critical points which agree well with values in the literature. Further, we estimate the associated critical exponents $\alpha$ and $\beta$ which turns out to be a challenging task for the CST approach.