Research on large-scale simulation method for quantum lattice models with strong randomness

本项目的目标如下：1)发展随机量子晶格模型的量子蒙特卡罗方法及其应用。2)开发了描述和处理随机量子晶格模型的XML语言和C++类库。3)开发用于各种物理量测量和分析的C++类库。4)面向大规模并行超级计算机和分布式计算机系统的仿真资源管理系统的开发。5)开发了随机系统仿真输出档案系统。对于1)，我们发展了长程相互作用系统的O(N)蒙特卡罗方法，如磁偶极子相互作用和RKKY相互作用，以及具有强空间各向异性或自旋各向异性的量子自旋系统的链Bethe方法和新的多体格林函数方法。我们还利用基于连续虚时间循环算法的量子蒙特卡罗模拟研究了杂质对非磁性自旋间隙量子自旋系统的影响。对于2)、3)、4)，我们扩展了现有的用于量子格子模型模拟的Alps框架，并进一步开发了一个新的调度程序Alps/Parapack，使我们能够高效地对具有强随机性的系统进行大规模并行模拟。5)我们开发并构建了一个存储模拟参数和模拟输出的数据库系统。我们还构建了一个用于访问数据库的图形用户界面。

The objectives of the project are as follows : 1) development of quantum Monte Carlo methods for random quantum lattice models and their applications. 2) development of XML language and C++ class libraries to describe and handle random quantum lattice models. 3) development of C++ class libraries for measurement and analysis of various physical quantities. 4) development of resource management system for simulations on massively parallel supercomputers and distributed computer systems. 5) development of archive system for output of simulations on random systems. As for 1), we have developed O(N) Monte Carlo method for long-range interacting systems, such as magnetic dipole and RKKY interactions, and the chain Bethe method and a new many-body Green's function method for quantum spin systems with strong spatial or spin anisotropy. We also investigated impurity effects to the non-magnetic spin gapped quantum spin systems by an extensive quantum Monte Carlo simulation based on the continuous-imaginary-time loop algorithm. For 2), 3), 4), we have extended the existing ALPS frame work, which is for simulation of quantum lattice models, and further developed a new scheduler, ALPS/parapack, which enables us to perform large-scale parallel simulations of systems with strong randomness efficiently For 5), we have developed and constructed a database system which archives parameters and outputs of simulations. We also have built a GUI interface for accessing the database.