The ground state phase diagram of the quantumJ1–J2 spin-1/2 Heisenberg antiferromagnet on an anisotropic square lattice

Abstract

We have studied the ground state phase diagram of the quantum spin-1/2 frustrated Heisenberg antiferromagnet on a square lattice by using theframework of the differential operator technique. The Hamiltonian is solvedby using an effective-field theory for a cluster with two spins (EFT-2). Themodel is described using the Heisenberg Hamiltonian with two competingantiferromagnetic interactions: nearest neighbor (NN) with different coupling strengthsJ1 andJ1′ alongthe x and y directions and next nearest neighbor (NNN) with couplingJ2. 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 ofλ andα: antiferromagnetic (AF), collinear antiferromagnetic (CAF)and quantum paramagnetic (QP). For an intermediate regionλ1 < λ < 1 we observe a QP state between the ordered AF and CAF phases, which disappears forλ above some critical value . We find a second-order phase transition between the AF and QP phases and a first-ordertransition between the CAF and QP phases. The boundaries between these orderedphases merge at the quantum triple point (QTP). Below this QTP there is again adirect first-order transition between the AF and CAF phases, with a behaviorapproximately described by the classical line .