Effect of anisotropy on the field induced quantum critical properties of the three dimensional s=1/2 Heisenberg model

TL;DR

This study explores how in-plane anisotropy influences the quantum critical behavior of a three-dimensional spin-1/2 Heisenberg antiferromagnet under magnetic field, revealing changes in universal properties and critical parameters.

Contribution

It provides an analytical expression for the gap exponent and demonstrates the impact of anisotropy on critical magnetic fields and universal behavior in the model.

Findings

In-plane anisotropy breaks U(1) symmetry, altering the gap exponent.

Critical magnetic field varies strongly with anisotropy.

Transverse structure factor diverges at the antiferromagnetic wave vector.

Abstract

The field induced quantum critical properties of the three dimensional spin-1/2 anisotropic antiferromagnetic Heisenberg model has been studied. We have investigated the quantum phase transition between the spiral order and field induced ferromagnetic order by means of Bose-Einstein condensation of magnons in terms of a bosonic representation. The effect of in-plane anisotropy on the critical properties has been studied via the bosonic model by Green's function approach. We have found an analytic expression for the gap exponent in addition to numerical results for the critical magnetic field in terms of anisotropy parameter. The in-plane anisotropy breaks the U(1) symmetry explicitly which changes the universal behavior by a drastic change on the gap exponent. Moreover, the critical magnetic field depends strongly on the in-plane anisotropies. The divergence of the transverse structure factor at the antiferromagnetic wave vector confirms the onset of the magnetic order which scales with the negative value of gap exponent as the magnetic field approaches the critical one. The transverse staggered magnetization as an order parameter vanishes with exponent $\beta=0.5$ when the magnetic field reaches its critical value in low field region.