The ground state phase diagram of the quantum J₁-J₂ spin-1/2 Heisenberg antiferromagnet on an anisotropic square lattice

We have studied the ground state phase diagram of the quantum spin-1/2 frustrated Heisenberg antiferromagnet on a square lattice by using the framework of the differential operator technique. The Hamiltonian is solved by using an effective-field theory for a cluster with two spins (EFT-2). The model is described using the Heisenberg Hamiltonian with two competing antiferromagnetic interactions: nearest neighbor (NN) with different coupling strengths J ₁ and J₁′ along the x and y directions and next nearest neighbor (NNN) with coupling J₂. We propose a functional for the free energy (similar to the Landau expansion) and using Maxwell construction we obtain the phase diagram in the (λ, α) space, where λ = J₁′/J₁ and α = J₂/J₁. We obtain three different states depending on the values of λ and α: antiferromagnetic (AF), collinear antiferromagnetic (CAF) and quantum paramagnetic (QP). For an intermediate region λ₁ < λ < 1 we observe a QP state between the ordered AF and CAF phases, which disappears for λ above some critical value . We find a second-order phase transition between the AF and QP phases and a first-order transition between the CAF and QP phases. The boundaries between these ordered phases merge at the quantum triple point (QTP). Below this QTP there is again a direct first-order transition between the AF and CAF phases, with a behavior approximately described by the classical line .