Effect of anisotropy on the field-induced quantum critical properties of the three-dimensionals=12Heisenberg model

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 β = 0.5 when the magnetic field reaches its critical value in low field region.

Phase diagram of J1-J2 transverse field Ising model on the checkerboard lattice: a plaquette-operator approach

“…As a result, the interplaquette interactions hybridize the ground state of a single plaquette with the corresponding excited eigenstates. In order to take into account the effect of inter-plaquette interactions, we implement a bosonization formalism 33 similar to what has been introduced as bond-operator representation of spin systems [34][35][36][37][38][39] . A boson is associated to each eigenstate |u of a single-plaquette Hamiltonian such that the eigenstate is created by the corresponding boson creation operator b † I,u acting on the vacuum,…”