| 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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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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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 / エネルギースケール / 角転送行列繰り込み群 / スケーリング / ＤMＲG / 格子系 / エネルキースケール / フラクタル / テンソルネットワーク / ＤＭＲＧ / 繰込み群 / 計算物理学 / 双曲変形 / 指数変形 / 一様性 / 正弦２乗変形 |
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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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