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

Abstract

The ground state phase diagram of the quantum spin-1/2 Heisenberg antiferromagnet in the presence of nearest-neighbor (J1) andnext-nearest-neighbor (J2) interactions (J1–J2 model) on a stacked square lattice, where we introduce an interlayer coupling throughnearest-neighbor bonds of strength , is studied within the framework of the differential operator technique.The Hamiltonian is solved by effective-field theory in a cluster withN = 4 spins (EFT-4). We obtain the sublattice magnetizationmA for the ordered phases: antiferromagnetic (AF) and collinear (CAF—collinearantiferromagnetic). We propose a functional for the free energyΨμ(mμ) (μ = A, B) to obtain thephase diagram in the λ–α plane, where and α = J2/J1. Dependingon the values of λ and α, we found different ordered states (AF and CAF) and a disorderedstate (quantum paramagnetic (QP)). For an intermediate regionα1c(λ) < α < α2c(λ) we observe a QP phasethat disappears for λ below some critical value . For α < α1c(λ) and α > α2c(λ), andbelow λ1, we have the AF and CAF semi-classically ordered states, respectively. Atα = α1c(λ) a second-order transition between the AF and QP states occurs and atα = α2c(λ) a first-order transition between the AF and CAF phases takes place. The boundariesbetween these ordered phases merge at the critical end point , where . Above this CEP there is again a direct first-order transition betweenthe AF and CAF phases, with a behavior described by the pointαc independentof λ ≥ λ1.