Optimization of tensor network states by means of a minimal principle and applications to quantum systems

通过最小原理优化张量网络状态及其在量子系统中的应用

• 批准号: 22540388
• 负责人: NISHINO Tomotoshi
• 金额: $ 2.58万
• 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: 2010
• 资助国家: 日本
• 起止时间: 2010-04-01 至 2013-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540388/
• 关键词: テンソル積状態; DMRG; 繰込み群; 双曲変形; エンタングルメント; 境界条件; 正弦２乗変形; 変分計算; ＤＭＲＧ; 繰り込み群; 最小作用; 時間発展; 双曲平面; 並列計算

The tensor network states has a hight potential of expressing or approximating a given quantum state wave function. For an efficient optimization of each local tensor, the construction of the environment around the tensor is important. In this study, we focus on the boundary condition, i.e. the smooth boundary condition, where the interaction parameter gradually decreases to zero toward the system boundary, the hyperbolic deformation, where the parameter increases to the boundary. These conditions are imposed to one dimensional free or correlated quantum systems. Under these deformation, despite of the non-uniformity in the Hamiltonian, the corresponding ground state is uniform, and the local tensors are optimized in a homogeneous manner. The fact is confirmed by means of the density matrix renormalization group, which is a representative numerical tool to optimize local tensors. Several other trials on the tensor network state are also reported.

张量网络态具有表达或近似给定量子态波函数的潜力。为了有效地优化每个局部张量，张量周围环境的构建是重要的。在这项研究中，我们专注于边界条件，即光滑的边界条件，其中的相互作用参数逐渐减少到零的系统边界，双曲线变形，其中的参数增加到边界。这些条件被施加到一维自由或相关量子系统。在这些变形下，尽管哈密顿量的非均匀性，相应的基态是均匀的，并且局部张量以均匀的方式被优化。这一事实是通过密度矩阵重整化群，这是一个有代表性的数值工具，以优化局部张量证实。还报道了张量网络状态的其他几个试验。

项目成果

Scaling Relation for Excitation Energy Under Hyperbolic Deformation

双曲线变形下激发能的标度关系

• 发表时间: 2010
• 期刊: Progress of Theoretical Physics
• 作者: Hiroshi Ueda;Hiroki Nakano;Koichi Kusakabe;Tomotoshi Nishino
• 通讯作者: Tomotoshi Nishino

Absence of Boundary Effect under Sine-Square Deformation

正弦平方变形下不存在边界效应

• 发表时间: 2011
• 作者: 佐光政人;湯川諭;Osamu Sano;T. Nishino
• 通讯作者: T. Nishino

Doubling of Entanglement Spectrum in Tensor Renormalization Group

• DOI: 10.1103/physrevb.89.075116
• 发表时间: 2013-06
• 期刊: Physical Review B
• 影响因子: 3.7
• 作者: H. Ueda;K. Okunishi;T. Nishino

Non-Uniform Deformation Applied to 1D Quantum Systems

非均匀变形应用于一维量子系统

• 发表时间: 2012
• 作者: 伊藤伸一;湯川諭;T. Nishino
• 通讯作者: T. Nishino

Connecting distant ends of 1D critical systems by SSD

通过 SSD 连接一维关键系统的远端

• 发表时间: 2011
• 期刊: Phys.Rev.E
• 作者: N.Tajima;R.Kato;S.Sugawara;Y.Nishio;K.Kajita;H. Akiba;Toshiya Hikihara
• 通讯作者: Toshiya Hikihara