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

本项目的主要目标如下：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XML语言和C++类库来描述和处理随机量子晶格模型。3)开发C++类库，用于测量和分析各种物理量。4)为大规模并行超级计算机和分布式计算机系统上的仿真开发资源管理系统。5)为随机系统的模拟输出开发存档系统。对于1），我们发展了适用于长程相互作用系统的O（N）Monte Carlo方法，如磁偶极子和RKKY相互作用，以及适用于强空间各向异性或自旋各向异性量子自旋系统的链式Bethe方法和一种新的多体绿色函数方法。我们还利用基于连续虚时间环算法的量子Monte Carlo模拟研究了杂质对非磁性自旋能隙量子自旋系统的影响。对于（2）、（3）、（4），我们扩展了现有的ALPS框架，这是用于量子晶格模型的模拟，并进一步开发了一个新的调度器，ALPS/parapack，这使我们能够有效地执行大规模的并行模拟系统的强随机性。我们还建立了一个访问数据库的GUI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.