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 Néel 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.
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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.