Direct extension of the density-matrix renormalization group method toward two-dimensional large quantum lattices and related high-performance computing
Direct extension of the density-matrix renormalization group method toward two-dimensional large quantum lattices and related high-performance computing
复制标题
密度矩阵重整化群方法向二维大量子晶格的直接扩展及相关高性能计算
DOI：
10.1007/s13160-011-0027-z
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发表时间：
2011
影响因子：
0.9
通讯作者：
Toshiyuki Imamura and Masahiko Machida
中科院分区：
文献类型：
--
作者：
Susumu Yamada;Masahiko Okumura;Toshiyuki Imamura and Masahiko Machida
密度矩阵重整化群（DMRG）方法被计算物理学家广泛用作探索大量子晶格模型中的基态的高精度工具，例如，海森堡和哈伯德模型，这是众所周知的标准模型，分别描述了固态中相互作用的自旋和电子。DMRG方法最初是为1-D晶格/链模型开发的，之后提出了一些具体的扩展到2-D晶格（n-leg ladder）模型。然而，在1-D模型中获得的高精度并不总是保证在其扩展版本中，因为该算法的原始精致的优点是部分丢失。因此，我们选择了另一种方式。它是DMRG方法的直接2-D扩展，而不是需要巨大的内存空间，但内存爆炸通过并行化DMRG代码并进行性能调整来解决。并行化的直接扩展DMRG显示出良好的精度，如1-D模型和良好的并行效率，随着保持的状态数的增加。这一成功保证了在不久的将来，当peta-flops并行超级计算机可用时，大型2-D（n-leg ladder）量子晶格模型的精确分析。
The density-matrix renormalization group (DMRG) method is widely used by computational physicists as a high accuracy tool to explore the ground state in large quantum lattice models, e.g., Heisenberg and Hubbard models, which are well-known standard models describing interacting spins and electrons, respectively, in solid states. After the DMRG method was originally developed for 1-D lattice/chain models, some specific extensions toward 2-D lattice (n-leg ladder) models have been proposed. However, high accuracy as obtained in 1-D models is not always guaranteed in their extended versions because the original exquisite advantage of the algorithm is partly lost. Thus, we choose an alternative way. It is a direct 2-D extension of DMRG method which instead demands an enormously large memory space, but the memory explosion is resolved by parallelizing the DMRG code with performance tuning. The parallelized direct extended DMRG shows a good accuracy like 1-D models and an excellent parallel efficiency as the number of states kept increases. This success promises accurate analysis on large 2-D (n-leg ladder) quantum lattice models in the near future when peta-flops parallel supercomputers are available.