Phase diagram of the spin-1/2 J₁-J₂-J₃ Heisenberg model on the square lattice

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We presents the results of an extensive numerical study of the phase diagram of the spin-1/2, J₁-J₂-J₃ Heisenberg model on a square lattice, for both ferromagnetic and antiferromagnetic nearest-neighbor interactions J₁, using exact diagonalization with periodic and twisted boundary conditions. Comparison is made with published spin wave calculations. We show that quantum fluctuations play a very important role, changing both the extent and the wave vector of classical spiral phases, and leading to new quantum phases where the classical spiral states have a high degeneracy. These include a new phase with small or vanishing spin-stiffness, in addition to known valence-bond-solid and bond-nematic phases.