CAS Key Laboratory of Vacuum Physics, School of Physical Sciences, University of Chinese Academy of Sciences, P. O. Box 4588, Beijing 100049, China.
Kavli Institute for Theoretical Sciences, and CAS Key Laboratory of Vacuum Physics, School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China.
Phys Rev E. 2017 May;95(5-1):052147. doi: 10.1103/PhysRevE.95.052147. Epub 2017 May 30.
The continuous imaginary-time quantum Monte Carlo method with the worm update algorithm is applied to explore the ground-state properties of the spin-1/2 Heisenberg model with antiferromagnetic (AF) coupling J>0 and ferromagnetic (F) coupling J^{'}<0 along zigzag and armchair directions, respectively, on honeycomb lattice. It is found that by enhancing the F coupling J^{'} between zigzag AF chains, the system is smoothly crossover from one-dimensional zigzag spin chains to a two-dimensional magnetic ordered state. In absence of an external field, the system is in a stripe-ordered phase. In the presence of uniform and staggered fields, the uniform and staggered out-of-plane magnetizations appear while the stripe order remains in the xy plane, and a second-order quantum phase transition (QPT) at a critical staggered field is observed. The critical exponents of correlation length for QPTs induced by a staggered field for the cases with J>0, J^{'}<0 and J<0, J^{'}>0 are obtained to be ν=0.70046(1) and 0.7086(3), respectively, indicating that both cases belong to O(3) universality. The corresponding dynamic and susceptibility exponent z and γ/ν are fitted to be 1.006572(9), 1.9412(2) and 1.004615(8), 1.96121(9) for the two cases, respectively. The scaling behavior in a staggered field is analyzed, and the ground-state phase diagrams in the plane of coupling ratio and staggered field are presented for two cases. The temperature dependence of susceptibility and specific heat of both systems in external magnetic fields is also discussed. A Kosterlitz-Thouless phase transition is found for the present system in a uniform field.
采用具有蠕虫更新算法的连续虚时间量子蒙特卡罗方法，分别研究了沿锯齿和扶手椅方向具有反铁磁（AF）耦合 J>0 和铁磁（F）耦合 J^{'}<0 的自旋 1/2 海森堡模型的基态性质在蜂窝晶格上。结果表明，通过增强锯齿形 AF 链之间的 F 耦合 J^{'}，系统从一维锯齿形自旋链平滑地转变为二维磁有序态。在没有外场的情况下，系统处于条纹有序相。在存在均匀和交错场的情况下，出现了均匀和交错的面外磁化，而条纹序保持在 xy 平面内，并观察到一个二级量子相变（QPT）在一个临界交错场。对于 J>0、J^{'}<0 和 J<0、J^{'}>0 情况下由交错场引起的 QPT 的关联长度临界指数，分别得到 ν=0.70046(1) 和 0.7086(3)，表明两种情况都属于 O(3) 普遍性。分别拟合了 z 和 γ/ν 的动态和磁化率指数为 1.006572(9)、1.9412(2)和 1.004615(8)、1.96121(9)。分析了在交错场中的标度行为，并给出了两种情况下的耦合比和交错场的基态相图。还讨论了两个系统在外磁场中的磁化率和比热随温度的变化。在均匀场中发现了本系统的 Kosterlitz-Thouless 相变。
