权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Extension of DMRG by explicit construction of Density Matrices

通过密度矩阵的显式构造来扩展 DMRG

基本信息

批准号：
11640376
负责人：
NISHINO Tomotoshi
金额：
$ 2.24万
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：
1999
资助国家：
日本
起止时间：
1999 至 2000
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640376/
关键词：
Density Matrix Renormalization Tensor Product Ising Model DMRG 3D Lattice Potts Model TPVA 繰り込み群 2次元格子

项目摘要

In the finite temperature density matrix renormalization group (DMRG) they normally construct the density matrices by cutting a cylinder which correspond ; to the finite temperature one-dimensional (ID) quantum systems. In this case, the topology of the 2D system (= cylinder) is different from the plane, conventional and simple construction of the density matrix is not always most efficient in the sense of free-energy minimum. This is because there is information exchange around the cylinder, which is not properly included by the conventional method. There is similar difficulty in DMRG for 3D classical systems.We thus return back to the principle of DMRG, we consider an efficient construction of the density matrix from the view point of the variational states represented as tensor product and their improvements. As a result, we obtained an equation that optimizes the tensor product state. In addition, we find that the equation can be solved numerically by way of the corner transfer renormalization group method (CTMRG).We apply the new variational method thus obtained, the tensor product variational approxi-mation (TPVA) to 3D Ising and Potts models, and obtained the transition temperatures and latent heats, that are comparable to those obtained by Monte Carlo simulations.We also drawed the phase diagram of the 16-vertex model by applying CTMRG method to the 16-vertex model, in the parameter region that is not investigated so far.

在有限温度密度矩阵重整化群（DMRG）中，他们通常通过切割对应的圆柱体来构造密度矩阵；到有限温度一维（ID）量子系统。在这种情况下，二维系统（=圆柱体）的拓扑与平面不同，密度矩阵的传统且简单的构造在自由能最小值的意义上并不总是最有效的。这是因为圆柱体周围存在信息交换，而传统方法无法正确包含该信息交换。 3D经典系统的DMRG也存在类似的困难。因此，我们回到DMRG的原理，从张量积表示的变分状态及其改进的角度考虑密度矩阵的有效构造。结果，我们得到了优化张量积状态的方程。此外，我们发现该方程可以通过角转移重正化群法（CTMRG）进行数值求解。我们将由此获得的新变分方法，即张量积变分近似（TPVA）应用到3D Ising和Potts模型中，获得了与蒙特卡罗模拟获得的转变温度和潜热相当的结果。我们还绘制了相图 16 顶点模型，将 CTMRG 方法应用于 16 顶点模型，在目前尚未研究的参数区域。