The anisotropic quantum spin-1/2 Heisenberg antiferromagnet in the presence of a longitudinal field on a bcc lattice

In this work we study the critical behavior of the quantum spin-1/2 anisotropic Heisenberg antiferromagnet in the presence of a longitudinal field on a body centered cubic (bcc) lattice as a function of temperature, anisotropy parameter (Δ)(Δ) and magnetic field (H  ), where Δ=0Δ=0 and 1 correspond the isotropic Heisenberg and Ising models, respectively. We use the framework of the differential operator technique in the effective-field theory with finite cluster of N  =4 spins (EFT-4). The staggered ms=(mA−mB)/2ms=(mA−mB)/2 and total m=(mA+mB)/2m=(mA+mB)/2 magnetizations are numerically calculated, where in the limit of ms→0ms→0 the critical line TN(H,Δ)TN(H,Δ) is obtained. The phase diagram in the T−HT−H plane is discussed as a function of the parameter ΔΔ for all values of H∈[0,Hc(Δ)]H∈[0,Hc(Δ)], where Hc(Δ)Hc(Δ) correspond the critical field (TN=0)(TN=0). Special focus is given in the low temperature region, where a reentrant behavior is observed around of H=Hc(Δ)≥Hc(Δ=1)=8JH=Hc(Δ)≥Hc(Δ=1)=8J in the Ising limit, results in accordance with Monte Carlo simulation, and also was observed for all values of Δ∈[0,1]Δ∈[0,1]. This reentrant behavior increases with increase of the anisotropy parameter ΔΔ. In the limit of low field, our results for the Heisenberg limit are compared with series expansion values.

► In the lat decade there has been a great interest in the physics of the quantum phase transition in spins system.
► Effective-field theory in cluster with N=4 spins is generalized to treat the quantum spin-1/2 Heisenberg model.
► We have obtained phase diagram at finite temperature for the quantum spin-1/2 antiferromagnet Heisenberg model as a bcc lattice.