New Trend in DMRG - from the Optimization of the Tensor Product Decomposition

DMRG新趋势——来自张量积分解的优化

基本信息

批准号：
17540327
负责人：
NISHINO Tomotoshi
金额：
$ 1.92万
依托单位：
Kobe University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2005
资助国家：
日本
起止时间：
2005 至 2006
项目状态：
已结题

项目摘要

From the view point of the tensor product variational method, we have developed new variants of the density matrix renormalization group (DMRG) method.1. The computational background of the product wave function renormalization group (PWFRG) method, which accelerate the numerical convergence of the infinite system algorithm in DMRG, is analytically given by way of the corner transfer matrix renormalization group (CTMRG) method. The width of the variational state in the form of matrix product is extended applying a special transfer matrix, which is created by applying renormalization matrices to the identity operator.2. The real time DMRG, which trace the time evolution of quantum states, has a problem of error stacking. In order to improve the problem, we have considered a kind of action, which is calculated from product of tensors on each time slice. Minimization of the action draws the time evolution of the system, and thus the numerical algorithm of the real time DMRG is reformulated as a minimization problem, which can be treated very rapidly by parallel computation.3. As a practical application of the CTMRG method, we observe the phase diagram of a 10-vertex model. As a result, we find a new critical point, which subject to the Ising universality class.4. As a joint research with Dr. Andre j Gendiar, we observe the domain wall energy of the two-dimensional ANNNI model by the DMRG method. Phase transition directly from the anti-phase to the disordered phase is observed, and the presence of the floating phase is excluded.

从张量产品变分方法的角度来看，我们开发了密度基质重质化组（DMRG）方法的新变体。1。通过角落传递矩阵重质化组（CTMRG）方法，分析给出了分析DMRG中无限系统算法的数值收敛的计算背景（PWFRG）方法。矩阵产物形式的变异状态的宽度将扩展使用特殊的传输矩阵，该矩阵是通过将重归于矩阵应用于身份操作员2。实时DMRG追踪量子状态的时间演变，存在错误堆叠的问题。为了改善问题，我们考虑了一种动作，该动作是根据每次切片的张量产物来计算的。动作的最小化吸引了系统的时间演变，因此将实时DMRG的数值算法重新构建为最小化问题，可以通过并行计算非常迅速地对待。3。作为CTMRG方法的实际应用，我们观察到10-Vertex模型的相图。结果，我们找到了一个新的关键点，该点受伊辛普遍性类别的约束。4。作为与Andre J Gendiar博士的联合研究，我们通过DMRG方法观察了二维Annni模型的域壁能量。直接观察到从反相到无序相的相变，排除了浮动阶段的存在。