The quantum J1−J′1−J2 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 J1 and J ′ 1 along x and y directions competing with a next-nearest-neighbor coupling J2 (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 ≃ 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 α c ≃ λ / 2 .