量子临界点动力学指数的随机近似
Stochastic approximation of dynamical exponent at quantum critical point
摘要：
我们发展了一个统一的有限尺度量子相变方法，不需要动力学指数$z$的先验知识。在量子蒙特卡罗模拟期间，温度通过Robbins-Monro随机近似方法自动调谐，与有限尺寸系统的最低间隙成比例。的动力学指数估计在一个简单的方式从系统的大小依赖的温度。作为我们新方法的一个示范，结合世界线量子Monte Carlo蠕虫算法，研究了均匀和交错磁场中的二维$S=1/2$量子$XY$模型.在没有均匀磁场的情况下，我们得到了在量子临界点$z=1$与洛伦兹不变性完全一致的结果，即，三维经典$XY$普适类。另一方面，在有限均匀磁场下，动力学指数变为2，并且具有有效维数$(2+2)$的平均场普适性支配量子相变。
英文摘要：
We have developed a unified finite-size scaling method for quantum phase transitions that requires no prior knowledge of the dynamical exponent $z$. During a quantum Monte Carlo simulation, the temperature is automatically tuned by the Robbins-Monro stochastic approximation method, being proportional to the lowest gap of the finite-size system. The dynamical exponent is estimated in a straightforward way from the system-size dependence of the temperature. As a demonstration of our novel method, the two-dimensional $S=1/2$ quantum $XY$ model in uniform and staggered magnetic fields is investigated in the combination of the world-line quantum Monte Carlo worm algorithm. In the absence of the uniform magnetic field, we obtain the fully consistent result with the Lorentz invariance at the quantum critical point, $z=1$, i.e., the three-dimensional classical $XY$ universality class. Under a finite uniform magnetic field, on the other hand, the dynamical exponent becomes two, and the mean-field universality with effective dimension $(2+2)$ governs the quantum phase transition.
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