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The quantum J_{1}-J_{1'}-J_{2} spin-1/2 Heisenberg antiferromagnet: A variational method study

The phase transition of the quantum spin-1/2 frustrated Heisenberg antiferroferromagnet on an anisotropic square lattice is studied by using a variational treatment. The model is described by the Heisenberg Hamiltonian with two antiferromagnetic interactions: nearest-neighbor (NN) with different coupling strengths J_{1} and J_{1'} along x and y directions competing with a next-nearest-neighbor coupling J_{2} (NNN). The ground state phase diagram in the (λ,α) space, where λ=J_{1'}/J_{1} and α=J_{2}/J_{1}, is obtained. Depending on the values of λ and α, we obtain three different states: antiferromagnetic (AF), collinear antiferromagnetic (CAF) and quantum paramagnetic (QP). For an intermediate region λ_{1}<λ<1 we observe a QP state between the ordered AF and CAF phases, which disappears for λ above some critical value λ_{1}. The boundaries between these ordered phases merge at the quantum critical endpoint (QCE). Below this QCE there is again a direct first-order transition between the AF and CAF phases, with a behavior approximately described by the classical line α_{c}{\simeq}λ/2.