论文标题
三角形耦合模型中的量子相变
Quantum phase transitions in the triangular coupled-top model
论文作者
论文摘要
我们研究了三个三角形上的三个大型旋转的耦合模型。根据耦合强度，存在三个阶段：磁磁相无序，铁磁相和沮丧的抗铁磁相，可以通过平均场进近方法来区分。顺磁 - 铁磁相过渡伴随着全局$ z_2 $对称性的破坏，而顺磁性抗磁性相变则伴随着全局$ z_2 $对称性的破坏。超出平均场贡献之外的高阶量子效应的确切分析结果，例如激发能，量子波动和von Neumann熵，可以通过热力学极限中的Holstein-Primakoff转换和符号转化来实现。在量子临界点附近，能量差距闭合，以及在某些正交和von Neumann熵中量子波动的差异。应特别注意抗铁磁阶段，在该阶段，几何挫败感会生效。抗铁磁阶段中的临界行为与顺磁性和铁磁阶段的临界行为完全不同，这突出了几何挫败感的重要性。三角形耦合模型提供了一个简单且可行的平台，用于研究量子相变和几何挫败感引起的新型关键行为。
We study the coupled-top model with three large spins located on a triangle. Depending on the coupling strength, there exist three phases: disordered paramagnetic phase, ferromagnetic phase, and frustrated antiferromagnetic phase, which can be distinguished by the mean-field approach. The paramagnetic-ferromagnetic phase transition is accompanied by the breaking of the global $Z_2$ symmetry, whereas the paramagnetic-antiferromagnetic phase transition is accompanied by the breaking of both the global $Z_2$ symmetry and the translational symmetry. Exact analytical results of higher-order quantum effects beyond the mean-field contribution, such as the excitation energy, quantum fluctuation, and von Neumann entropy, can be achieved by the Holstein-Primakoff transformation and symplectic transformation in the thermodynamic limit. Near the quantum critical point, the energy gap closes, along with the divergence of the quantum fluctuation in certain quadrature and von Neumann entropy. Particular attention should be paid to the antiferromagnetic phase, where geometric frustration takes effect. The critical behaviors in the antiferromagnetic phase are quite different from those in the paramagnetic and ferromagnetic phases, which highlight the importance of geometric frustration. The triangular coupled-top model provides a simple and feasible platform to study the quantum phase transition and the novel critical behaviors induced by geometric frustration.
