Quantum Monte Carlo study of the spin-1/2 honeycomb Heisenberg model with mixed
antiferromagnetic and ferromagnetic interactions in external magnetic fields
Yi-Zhen Huang
CAS Key Laboratory of Vacuum Physics, School of Physical Sciences, University of Chinese Academy of Sciences,
P. O. Box 4588, Beijing 100049, China
Gang Su*
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
(Received 14 December 2016; revised manuscript received 19 April 2017; published 30 May 2017)

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 withJ > 0, J < 0 andJ < 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.