2016 Fiscal Year Final Research Report
Renormalization group analysis of energy-scale deformation by means of tensor-network formulations
| Project/Area Number |
25400401
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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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 |
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| Research Collaborator |
Gendiar Andrej Slovak Academy of Sciences, Independent Researcher
Krcmar Roman Slovak Academy of Sciences, Researcher
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Keywords | エネルギースケール変形 / テンソルネットワーク形式 / 繰り込み群 / エンタングルメント / 双曲格子 / 相転移 / 臨界指数 / エントロピー |
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| Outline of Final Research Achievements |
We investigated several types of lattice models under the energy scale deformation, where the local interaction strength is modulated slowly compared with the lattice constant, by means of numerical calculation assisted by the tensor network formulations. From the obtained thermal equilibrium states, behavior of entanglement entropy is analyzed with respect to temperature and parameters. In case of Ising model on hyperbolic lattices, which has a small negative curvature, its critical behavior is mean-field like, and the correlation length is bounded around the curvature radius even at the phase transition point. In the study of discrete Heisenberg model on two-dimensional lattice, various types of phase transitions are observed according to the manner of discretization. For example, we observed 1st order phase transition, and the Berezinskii-Kosterlitz-Thouless one, etc. We have also developed numerical methods for fractal systems and for tracing wave packets on 1D lattice.
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| Free Research Field |
計算物理学
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