Theoretical Condensed Matter Physics and Computational Materials Physics Laboratory, School of Physics, University of Chinese Academy of Sciences, P. O. Box 4588, Beijing 100049, China.
Department of Physics and Beijing Laboratory of Opto-electronic Functional Materials & Micro-nano Devices, Renmin University of China, Beijing 100872, China.
Phys Rev E. 2016 Jun;93(6):062110. doi: 10.1103/PhysRevE.93.062110. Epub 2016 Jun 6.
The quantum phase transition, scaling behaviors, and thermodynamics in the spin-1/2 quantum Heisenberg model with antiferromagnetic coupling J>0 in the armchair direction and ferromagnetic interaction J^{'}<0 in the 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 ratios 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, 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 compared with the experimental data to give the magnetic parameters of both compounds.
采用连续时间量子蒙特卡罗方法系统地研究了具有反铁磁耦合 J>0 的扶手椅方向和铁磁相互作用 J^{'}<0 的锯齿方向的 honeycomb 晶格上的自旋-1/2 量子海森堡模型中的量子相变、标度行为和热力学。通过计算不同晶格尺寸下不同耦合比α=J^{'}/J 下各向的 Binder 比 Q_{2}和自旋刚度 ρ，我们发现从二聚相到条纹相的量子相变发生在量子临界点α_{c}=-0.93。通过对 Q_{2}、ρ_{x}和 ρ_{y}的有限尺寸标度分析，我们确定了与关联长度 ν 相关的临界指数为 0.7212(8)，表明该相变属于经典海森堡 O(3) 普遍性。在二聚相中观察到零磁化平台，其宽度随α的增加而减小。在耦合比 α-磁场 h 平面上得到了一个相图，其中识别出了四个相，包括二聚相、条纹相、倾斜条纹相和极化相。还揭示了不同 α 的比热 C(T)随温度的变化在一个点上精确相交，类似于不同压力下的液体 ^{3}He 和不同磁场下的几种磁性化合物。仔细分析了 Q_{2}、ρ和 C(T)的标度行为。将磁化率与实验数据进行比较，给出了两种化合物的磁性参数。
