The quantum spin-1/2 J1-J2 antiferromagnet on a stacked square lattice: a study of effective-field theory in a finite cluster

The ground state phase diagram of the quantum spin-1/2 Heisenberg antiferromagnet in the presence of nearest-neighbor (J(1)) and next-nearest-neighbor (J(2)) interactions (J(1)-J(2) model) on a stacked square lattice, where we introduce an interlayer coupling through nearest-neighbor bonds of strength J(perpendicular to), is studied within the framework of the differential operator technique. The Hamiltonian is solved by effective-field theory in a cluster with N = 4 spins (EFT-4). We obtain the sublattice magnetization m(A) for the ordered phases: antiferromagnetic (AF) and collinear (CAF-collinear antiferromagnetic). We propose a functional for the free energy Psi(mu)(m(mu)) (mu = A, B) to obtain the phase diagram in the lambda-alpha plane, where lambda = J(perpendicular to)/J(1) and alpha = J(2)/J(1). Depending on the values of lambda and alpha, we found different ordered states (AF and CAF) and a disordered state (quantum paramagnetic (QP)). For an intermediate region alpha(1c)(lambda) < alpha < alpha(2c)(lambda) we observe a QP phase that disappears for lambda below some critical value lambda(1) similar or equal to 0.67. For alpha < alpha(1c)(lambda) and alpha > alpha(2c)(lambda), and below lambda(1), we have the AF and CAF semi-classically ordered states, respectively. At alpha = alpha(1c)(lambda) a second-order transition between the AF and QP states occurs and at alpha = alpha(2c)(lambda) a first-order transition between the AF and CAF phases takes place. The boundaries between these ordered phases merge at the critical end point CEP = (lambda(1), alpha(c)), where alpha(c) similar or equal to 0.56. Above this CEP there is again a direct first-order transition between the AF and CAF phases, with a behavior described by the point ac independent of lambda >= 1.