Thermal phase transition of generalized Heisenberg models for SU(N) spins on square and honeycomb lattices
Thermal phase transition of generalized Heisenberg models for SU(N) spins on square and honeycomb lattices
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DOI：
10.1103/physrevb.91.094414
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发表时间：
2015-03
影响因子：
3.7
通讯作者：
Takafumi J. Suzuki;K. Harada;H. Matsuo;S. Todo;N. Kawashima
中科院分区：
文献类型：
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作者：
Takafumi J. Suzuki;K. Harada;H. Matsuo;S. Todo;N. Kawashima
我们分别研究了正方形和蜂窝格子上的四体和六体相互作用的SU（N）海森堡模型中到价键固相的热相变。在这两种情况下，热相变发生伴随着晶格的旋转对称性破缺。我们进行量子蒙特卡罗计算，以澄清模型的关键属性。估计的临界指数表明，正方形和蜂窝格点情况的普适类分别与具有Z_4 $对称破缺场的经典$XY$模型和三态Potts模型的普适类相同。在正方形晶格的情况下，热指数，$\nu$，单调增加的系统接近量子临界点，而临界指数的值，$\eta$和$\gamma/\nu$，保持不变。通过有限尺度分析，我们发现系统具有弱普适性，因为Z_4破缺场总是边缘的。相比之下，在蜂窝格点的情况下，$\nu$表现出一个恒定的值，即使在量子临界点附近，因为在SU（3）和SU（4）的情况下，$Z_3$场仍然是相关的。
We investigate thermal phase transitions to a valence-bond solid phase in SU(N) Heisenberg models with four- or six-body interactions on a square or honeycomb lattice, respectively. In both cases, a thermal phase transition occurs that is accompanied by rotational symmetry breaking of the lattice. We perform quantum Monte Carlo calculations in order to clarify the critical properties of the models. The estimated critical exponents indicate that the universality classes of the square- and honeycomb-lattice cases are identical to those of the classical $XY$ model with a $Z_4$ symmetry-breaking field and the 3-state Potts model, respectively. In the square-lattice case, the thermal exponent, $\nu$, monotonically increases as the system approaches the quantum critical point, while the values of the critical exponents, $\eta$ and $\gamma/\nu$, remain constant. From a finite-size scaling analysis, we find that the system exhibits weak universality, because the $Z_4$ symmetry-breaking field is always marginal. In contrast, $\nu$ in the honeycomb-lattice case exhibits a constant value, even in the vicinity of the quantum critical point, because the $Z_3$ field remains relevant in the SU(3) and SU(4) cases.