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Quantum phase transition, universality and scaling behaviors in the spin-1/2 Heisenberg model with ferromagnetic and antiferromagnetic competing interactions on honeycomb lattice

The quantum phase transition, scaling behaviors, and thermodynamics in the spin-1/2 quantum Heisenberg model with antiferromagnetic coupling $J>0$ in armchair direction and ferromagnetic interaction $J'<0$ in zigzag direction on a honeycomb lattice are systematically studied using the continuous-time quantum Monte Carlo method. By calculating the Binder ratio $Q_{2}$ and spin stiffness $ρ$ in two directions for various coupling ratio $α=J'/J$ under different lattice sizes, we found that a quantum phase transition from the dimerized phase to the stripe phase occurs at the quantum critical point $α_c=-0.93$. Through the finite-size scaling analysis on $Q_{2}$, $ρ_{x}$ and $ρ_{y}$, we determined the critical exponent related to the correlation length $ν$ to be 0.7212(8), implying that this transition falls into a classical Heisenberg O(3) universality. A zero magnetization plateau is observed in the dimerized phase, whose width decreases with increasing $α$. A phase diagram in the coupling ratio $α$-magnetic field $h$ plane is obtained, where four phases, including dimerized, stripe, canted stripe and polarized phases are identified. It is also unveiled that the temperature dependence of the specific heat $C(T)$ for different $α$'s intersects precisely at one point, similar to that of liquid $^{3}$He under different pressures and several magnetic compounds under various magnetic fields. The scaling behaviors of $Q_{2}$, $ρ$ and $C(T)$ are carefully analyzed. The susceptibility is well compared with the experimental data to give the magnetic parameters of both compounds.