Phase Transition of Heisenberg Model on Honeycomb Lattice with Mixed Interactions by Quantum Monte Carlo*

We studied the quantum Heisenberg model with J>0 and J'<0 along the zigzag and armchair directions on honeycomb lattice with worm monte carlo method. By size extrapolation of the stripe order, we found that when tuning J' with J fixed the system crossovers from a disordered 1D system to a striped ordered 2D one. An uniform magnetic field h perpendicular to the plane tilts the spins along the field's direction and keeps the transverse components stripe ordered. As long as h ≧2J, all the spins are polarized.

By measuring the spin stiffness ρ of honeycomb systems with J>0, J'<0 and J<0, J'>0 of unit strength, we found that a second order quantum phase transition induced by a staggered magnetic field h_s . With the applications of finite size scaling and Robbins-Monro stochastic approximation methods, the transition points and critical exponents are calculated to be h_sc=0.423831(2) and 0.496884(4), ν=0.70046(1) and 0.7086(3), z=1.006572(9) and 1.004615(8), γ/ν=1.9412(2) and 1.96121(9) respectively, indicating these two O(3) universality. And finite temperature features along with a KT phase transition under uniform field have also been discussed in our work.