The quantum J1−J′1−J2 spin-1/2 Heisenberg antiferromagnet: A variational method study

•We study the J1−J′1−J2J1−J′1−J2 model on an anisotropic square lattice by using a variational method.•We obtain the ground phase diagram in the λαλα plane (λ=J′1/J1λ=J′1/J1 and α=J2/J1α=J2/J1).•A comparison with other results of the J1−J′1−J2J1−J′1−J2 model.•We obtain the behavior of the order parameter and internal energy as a function of the λλ and αα parameters.

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 J1 and J′1J′1 along x and y directions competing with a next-nearest-neighbor coupling J2 (NNN). The ground state phase diagram in the (λ,αλ,α) space, where λ=J′1/J1λ=J′1/J1 and α=J2/J1α=J2/J1, is obtained. Depending on the values of λλ and αα, we obtain three different states: antiferromagnetic (AF), collinear antiferromagnetic (CAF) and quantum paramagnetic (QP). For an intermediate region λ1<λ<1λ1<λ<1 we observe a QP state between the ordered AF and CAF phases, which disappears for λλ above some critical value λ1≃0.53λ1≃0.53. 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 αc≃λ/2αc≃λ/2.