Frustrated spin-1/2 J1-J2 Heisenberg ferromagnet on the square lattice studied via exact diagonalization and coupled-cluster method

We investigate the ground-state magnetic order of the spin-1/2 J(1)-J(2) Heisenberg model on the square lattice with ferromagnetic nearest-neighbor exchange J(1)<0 and frustrating antiferromagnetic next-nearest-neighbor exchange J(2)>0. We use the coupled-cluster method to high orders of approximation and Lanczos exact diagonalization of finite lattices of up to N=40 sites in order to calculate the ground-state energy, the spin-spin correlation functions, and the magnetic order parameter. We find that the transition point at which the ferromagnetic ground state disappears is given by J(2)(c1)=0.393 vertical bar J(1)vertical bar (exact diagonalization) and J(2)(c1)=0.394 vertical bar J(1)vertical bar (coupled-cluster method). We compare our results for ferromagnetic J(1) with established results for the spin-1/2 J(1)-J(2) Heisenberg model with antiferromagnetic J(1). We find that both models (i.e., ferro-and antiferromagnetic J(1)) behave similarly for large J(2), although significant differences between them are observed for J(2)/vertical bar J(1)vertical bar less than or similar to 0.6. Although the semiclassical collinear magnetic long-range order breaks down at J(2)(c2)approximate to 0.6J(1) for antiferromagnetic J(1), we do not find a similar breakdown of this kind of long-range order until J(2)similar to 0.4 vertical bar J(1)vertical bar for the model with ferromagnetic J(1). Unlike the case for antiferromagnetic J(1), if an intermediate disordered phase does occur between the phases exhibiting semiclassical collinear stripe order and ferromagnetic order for ferromagnetic J(1) then it is likely to be over a very small range below J(2)similar to 0.4 vertical bar J(1)vertical bar.