In this talk I present the phase diagram of the frustrated spin-1/2 XY and Heisenberg models on the honeycomb lattice, obtained by using accurate correlated wave functions and Variational Monte Carlo simulations. Upon increasing the frustration, these models show a very rich sequence of spin-ordered phases and a spin-liquid state is energetically favorable in a small region of intermediate frustration.1 In my investigation, I consider an unprecedented broad variety of spin (spiral) waves. These ordered phases are represented by classically ordered states supplemented with a long-range Jastrow factor, which includes relevant correlations and dramatically improves the description provided by the purely classical solution of the models. The construction of the spin-liquid state is based on a spin decomposition in terms of fermions, experiencing a Gutzwiller projection and long-range Jastrow correlations. In comparison with the classical phase diagram, the quantum fluctuations prolong the stability of the NĂ©el antiferromagnet and favor a stripe order for intermediate and quite strong frustration. The spiral waves are ground state for strong frustration and the 120th-order becomes the lowest-energy phase for very strong frustration. I also discuss connections with experiments on magnetically frustrated systems.

J. Carrasquilla, A. Di Ciolo, F. Becca, V. Galitski, and M. Rigol, arXiv:1307.2267 (2013); A. Di Ciolo, J. Carrasquilla, F. Becca, M. Rigol, and V. Galitski, in preparation.