Nonomura Yoshihiko, Tomita Yusuke
International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Ibaraki 305-0044, Japan.
College of Engineering, Shibaura Institute of Technology, Saitama 337-8570, Japan.
Phys Rev E. 2020 Mar;101(3-1):032105. doi: 10.1103/PhysRevE.101.032105.
Although the nonequilibrium-relaxation (NER) method has been widely used in Monte Carlo studies on phase transitions in classical spin systems, such studies have been quite limited in quantum phase transitions. The reason is that the relaxation process based on cluster-update quantum Monte Carlo (QMC) algorithms, which are now standards in Monte Carlo studies on quantum systems, has been considered "too fast" for such analyses. Recently, the present authors revealed that the NER process in classical spin systems based on cluster-update algorithms is characterized by stretched-exponential critical relaxation, rather than conventional power-law relaxation in local-update algorithms. In the present article, we show that this is also the case in quantum phase transitions analyzed with the cluster-update QMC. As the simplest example of isotropic quantum spin models that exhibit quantum phase transitions, we investigate the Néel-dimer quantum phase transition in the two-dimensional S=1/2 columnar-dimerized antiferromagnetic Heisenberg model with the continuous-time loop algorithm, and we confirm stretched-exponential critical relaxation consistent with the three-dimensional classical Heisenberg model in the Swendsen-Wang algorithm.
尽管非平衡弛豫（NER）方法已在经典自旋系统相变的蒙特卡罗研究中广泛使用，但此类研究在量子相变方面相当有限。原因在于，基于团簇更新量子蒙特卡罗（QMC）算法的弛豫过程，而这种算法目前是量子系统蒙特卡罗研究的标准方法，被认为对于此类分析“太快”。最近，本文作者揭示，基于团簇更新算法的经典自旋系统中的NER过程，其特征是拉伸指数临界弛豫，而非局部更新算法中的传统幂律弛豫。在本文中，我们表明在用团簇更新QMC分析的量子相变中也是如此。作为表现出量子相变的各向同性量子自旋模型的最简单例子，我们用连续时间回路算法研究二维S = 1/2柱状二聚化反铁磁海森堡模型中的奈尔二聚体量子相变，并证实与斯文森 - 王算法中的三维经典海森堡模型一致的拉伸指数临界弛豫。
