Optimization of tensor network states by means of a minimal principle and applications to quantum systems
| Project/Area Number |
22540388
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Kobe University |
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Principal Investigator |
NISHINO Tomotoshi 神戸大学, 理学(系)研究科(研究院), 准教授 (00241563)
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| Research Collaborator |
ANDREJ Gendiar Slovak Academy of Sciences, Independent Researcher
ROMAN Krcmar Slovak Academy of Sciences, Researcher
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| Project Period (FY) |
2010-04-01 – 2013-03-31
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 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 |
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| Research Abstract |
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.
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Report
(4 results)
Research Products
(33 results)
