CONICET | Buscador de Institutos y Recursos Humanos

We study the occurrence of symmetry breakings, at zero and finite temperatures, in the $J_1-J_3$ antiferromagnetic Heisenberg model on the square lattice using Schwinger boson mean field theory. For spin-$rac{1}{2}$ the ground state breaks always the $SU(2)$ symmetry with a continuous quasi-critical transition at $J_3/J_1sim0.38$, from N´eel to spiral long range order, although local spin fluctuations considerations suggest an intermediate disordered regime around $0.35 lesssim J_3/J_1 lesssim 0.5$, in qualitative agreement with recent numerical results. At low temperatures we find a $Z_2$ broken symmetry region with short range spiral order characterized by an Ising-like nematic order parameter that compares qualitatively well with classical Monte Carlo results. At intermediate temperatures the phase diagram shows regions with collinear short range orders: for $J_3/J_11$ a novel phase consisting of four decoupled third neighbour sublattices with N´eel $(pi,pi)$ correlations in each one. We conclude that the effect of quantum and thermal fluctuations is to favour collinear correlations even in the strongly frustrated regime.