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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.

从张量积变分方法的角度出发，我们开发了密度矩阵重整化群（DMRG）方法的新变体。 1．通过角转移矩阵重正化群(CTMRG)方法，分析给出了乘积波函数重正化群(PWFRG)方法的计算背景，该方法加速了DMRG中无限系统算法的数值收敛。采用特殊的传递矩阵扩展了矩阵乘积形式的变分状态的宽度，该传递矩阵是通过将重整化矩阵应用于恒等算子而创建的。 2．追踪量子态时间演化的实时 DMRG 存在错误叠加问题。为了改善这个问题，我们考虑了一种动作，它是根据每个时间片上张量的乘积来计算的。动作的最小化吸引了系统的时间演化，因此实时DMRG的数值算法被重新表述为一个最小化问题，可以通过并行计算非常快速地处理。 3．作为 CTMRG 方法的实际应用，我们观察 10 顶点模型的相图。结果，我们发现了一个新的临界点，该临界点服从伊辛普适性等级。 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模型的畴壁能量。观察到直接从反相到无序相的相变，并且排除了浮动相的存在。