Study on Phase Transitions and Dynamics of Spin System with Long-range Interactions

长期以来，模拟具有远程相互作用的自旋系统一直是非常困难的，因为相互作用的数量与自旋数量的平方成正比。本文提出了一种适用于一般远程相互作用系统的n阶蒙特卡罗方法。我们还开发了一种通用的算法，使蒙特卡罗方法的拒绝率最小。此外，我们揭示了自旋-冰的低温相位和量子声子在自旋-佩尔斯系统中的作用，并提出了测量纠缠熵和局部Z_2 Berry相位的方法。

It has long been very difficult to simulate spin systems with long-range interactions since the number of interactions increases proportional to the square of the number of spins. We have developed an Order-N Monte Carlo method for generic long-range interacting system. We have also developed a versatile algorithm, which minimizes the rejection rate in Monte Carlo method. In addition, we have revealed the low-temperature phase of the spin-ice and the effect of quantum phonon in spin-Peierls system, and proposed methods to measure the entanglement entropy and local Z_2 Berry phase.