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Wide applications of the renormalization group

Research Project

Project/Area Number 14340077
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field 素粒子・核・宇宙線
Research InstitutionKobe University

Principal Investigator

SONODA Hidenori  Kobe University, Physics Department, Assoc. Professor., 理学部, 助教授 (20291966)

Co-Investigator(Kenkyū-buntansha) LIM C.s.  Kobe University, Physics Department, Professor, 理学部, 教授 (80201870)
HARIMA Hisatomo  Kobe University, Physics Department, Professor, 理学部, 教授 (50211496)
KUBOKI Kazuhiro  Kobe University, Physics Department, Assoc. Professor, 理学部, 助教授 (50231296)
NISHINO Tomotoshi  Kobe University, Physics Department, Assoc. Professor, 理学部, 助教授 (00241563)
SAKAMOTO Makoto  Kobe University, Physics Department, Assistant Professor, 理学部, 助手 (30183817)
斯波 弘行  神戸大学, 理学部, 教授 (30028196)
Project Period (FY) 2002 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥14,600,000 (Direct Cost: ¥14,600,000)
Fiscal Year 2005: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2004: ¥4,000,000 (Direct Cost: ¥4,000,000)
Fiscal Year 2003: ¥4,000,000 (Direct Cost: ¥4,000,000)
Fiscal Year 2002: ¥5,100,000 (Direct Cost: ¥5,100,000)
Keywordsexact renormalization group / density matrix renormalization group / gauge theories / tensor product variational method / 繰り込み / カイラル対称性 / 密度行列くりこみ群 / f電子系 / 磁気異方性 / 繰り込み群 / 完璧作用
Research Abstract

We have applied renormalization group (RG) techniques to both quantum field theory and statistical physics. The research in quantum field theory was led by Sonoda, and that in statistical physics by Nishino.
In the applications to quantum field theory, the following results have been obtained:
1. Parametrization of the solutions to the exact RG equations was introduced by examining the behavior of the solutions at a large momentum cutoff
2. The exact RG equation has been reformulated as an integral equation, which gives a formal perturbative solution.
3. The parametrization described in 1 has been applied to QED. The Ward identities constrain the parameters.
In the applications to statistical physics, the following results have been obtained:
1. Avery fast numerical method of the product wave function RG has been developed.
2. Generalizing the matrix products to tensor products, we have formulated the tensor product RG variational method, which can be considered as an extension of the density matrix RG method to higher dimensional systems.
3. Extending the density matrix RG method, we have obtained the stochastic light-cone density matrix RG and the method of snapshot generation. These have been applied to statistical systems, resulting in phase diagrams of 2-and 3-dimensional ANNNI models, and the symmetric 16-vertex model.

Report

(5 results)
  • 2005 Annual Research Report   Final Research Report Summary
  • 2004 Annual Research Report
  • 2003 Annual Research Report
  • 2002 Annual Research Report
  • Research Products

    (41 results)

All 2006 2005 2004 2003 2002 Other

All Journal Article (31 results) Book (1 results) Publications (9 results)

  • [Journal Article] Product wave function renormalization group : construction from the matrix product point of view2006

    • Author(s)
      K.Ueda, T.Nishino., K.Okunishi, Y.Hieida, R.Derian, A.Gendiar
    • Journal Title

      J. Phys. Soc. Jpn. 75

      Pages: 14003-14003

    • NAID

      110003482826

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Product wave function renormalization group : construction from the matrix product point of view,2006

    • Author(s)
      K.Ueda, T.Nishino, K.Okunishi, Y.Hieida, R.Derian, A.Gendiar
    • Journal Title

      J. Phys. So. Jpn. 75

      Pages: 14003-14003

    • NAID

      110003482826

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Product Wave Function Renormalization Group : construction from the matrix product point of view2006

    • Author(s)
      K.Ueda, T.Nishino, K.Okunishi, Y.Hieida, R.Derian, A.Gendiar
    • Journal Title

      J.Phys.Soc.Jpn. 75

      Pages: 14003-14003

    • NAID

      110003482826

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Microscopic origin of magnetic anisotropy in f-electron systems2005

    • Author(s)
      T.Takimoto
    • Journal Title

      Physica B 359-361

      Pages: 747-749

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Estimation of the magnetic critical exponent by tensor product variational approach2005

    • Author(s)
      A.Gendiar, T.Nishino, R.Derian
    • Journal Title

      Acta Physica Slovaca 55

      Pages: 141-141

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Snapshot observation for 2D classcial lattice models by CTMRG2005

    • Author(s)
      K.Ueda, R.Otani, Y.Nishio, A.Gendiar, T.Nishino
    • Journal Title

      J. Phys. Soc. Jpn. supplement 74

      Pages: 111-114

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Phase diagram of the 3D ANNNI model2005

    • Author(s)
      A.Gendiar, T.Nishino
    • Journal Title

      Phys. Rev. B 71

      Pages: 24404-24404

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Supersymmetry in gauge theories with extra dimensions2005

    • Author(s)
      C.S.Lim, T.Nagasawa, M.Sakamoto, H.Sonoda
    • Journal Title

      Phys. Rev. D 72

      Pages: 64006-64006

    • NAID

      110006417158

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Microscopic origin of magnetic anisotropy in f-electron systems,2005

    • Author(s)
      T.Takimoto
    • Journal Title

      Physica B 359-361

      Pages: 747-749

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Estimation of magnetic critical exponent by tensor product variational approach,2005

    • Author(s)
      A.Gendiar, T.Nishino, R.Derian
    • Journal Title

      Acta Physica Slovaca 55

      Pages: 141-141

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Snapshot observation for 2D classical lattice models by CTMRG,2005

    • Author(s)
      K.Ueda, R.Otani, Y.Nishio, A.Gendiar, T.Nishino
    • Journal Title

      J. Phys. Soc. Jpn. 74 supplement

      Pages: 111-114

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Phase diagram of the 3D ANNNI model,2005

    • Author(s)
      A.Gendiar, T.Nishino
    • Journal Title

      Phys. Rev. B71

      Pages: 24404-24404

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Supersymmetry in gauge theories with extra dimensions,2005

    • Author(s)
      C.S.Lim, T.Nagasawa, M.Sakamoto, H.Sonoda
    • Journal Title

      Phys. Rev. D72

      Pages: 64006-64006

    • NAID

      110006417158

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Supersymmetry in Gauge Theories with Extra Dimensions2005

    • Author(s)
      C.S.Lim, T.Nagasawa, M.Sakamoto, H.Sonoda
    • Journal Title

      Phys.Rev.D 72

      Pages: 64006-64006

    • NAID

      110006417158

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Phase Diagram of the 3D ANNNI Model2005

    • Author(s)
      A.Gendiar, T.Nishino
    • Journal Title

      Physical Review B71

      Pages: 24404-24404

    • Related Report
      2004 Annual Research Report
  • [Journal Article] 密度行列繰り込み群といくつかの変分原理2004

    • Author(s)
      西野 友年
    • Journal Title

      数理解析研究所講究録 1386

      Pages: 117-117

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Density matrix renormalization group and variational principles, (in Japanese)2004

    • Author(s)
      T.Nishino
    • Journal Title

      RIMS colloquia vol. 1386

      Pages: 117-117

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] 密度行列繰り込み群と幾つかの変分原理2004

    • Author(s)
      西野 友年
    • Journal Title

      数理解析研究所講究録 1386

      Pages: 117-117

    • Related Report
      2004 Annual Research Report
  • [Journal Article] 連続極限のとり方2004

    • Author(s)
      園田 英徳
    • Journal Title

      素粒子論研究 109巻5号

      Pages: 35-35

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Bootstrapping perturbative perfect actions2003

    • Author(s)
      H.Sonoda
    • Journal Title

      Phys. Rev. D67

      Pages: 65011-65011

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Stochastic light-cone CTMRG : a new DMRG approach to stochastic models2003

    • Author(s)
      A.Kemper, A.Gendiar, T.Nishino
    • Journal Title

      J. Phys. A : Math. Gen. 36

      Pages: 29-29

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Stable optimization of tensor product variational functions2003

    • Author(s)
      A.Gendiar, T.Nishino
    • Journal Title

      Prog. Theo. Phys. 110

      Pages: 6901-6901

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Three-dimensional noolinear sigma models in the Wilsonian renormalization method2003

    • Author(s)
      E.Itou, K.Higashijima
    • Journal Title

      Prog. Theor. Phys. 110

      Pages: 563-563

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Bootstrapping perturbative perfect actions,2003

    • Author(s)
      H.Sonoda
    • Journal Title

      Phys. Rev. D67

      Pages: 65011-65011

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Stable optimization of tensor product variational functions,2003

    • Author(s)
      A.Gendiar, T.Nishino
    • Journal Title

      Prog. Theor. Phys. 110

      Pages: 6901-6901

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Three-dimensional nonlinear sigma models in the Wilsonian renormalization method,2003

    • Author(s)
      E.Itou, K.Higashijima
    • Journal Title

      Prog. Theor. Phys. 110

      Pages: 563-563

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Latent heat observation of the q=3,4, and 5 Potts models by tensor product variational approach2002

    • Author(s)
      A.Gendiar, T.Nishino
    • Journal Title

      Phys. Rev. E65

      Pages: 46702-46702

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Latent heat observation of the q=3,4, and 5 Potts models by tensor product variational approach,2002

    • Author(s)
      A.Gendiar, T.Nishino
    • Journal Title

      Phys. Rev. E65

      Pages: 46702-46702

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Microscopic origin of magnetic anisotropy in f-electron systems

    • Author(s)
      T.Takimoto
    • Journal Title

      Physica B (accepted for publication)(未定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Estimation of the Magnetic Critical Exponent by Tensor Product Variational Approach

    • Author(s)
      A.Gendiar, T.Nishino, R.Derian
    • Journal Title

      Acta Physica Slovaca (accepted for publication)(未定)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Snapshot Observation for 2D Classical Lattice Models by CTMRG

    • Author(s)
      K.Ueda, R.Otani, Y.Nishino, A.Gendiar, T.Nishino
    • Journal Title

      JPSJ supplement (accepted for publication)(未定)

    • Related Report
      2004 Annual Research Report
  • [Book] 相互作用する電子2003

    • Author(s)
      斯波 弘行
    • Total Pages
      80
    • Publisher
      岩波書店
    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Publications] 西野友年: "密度行列繰り込み群と幾つかの変分原理"数理解析研究会 Proceedings in Japanese. (in press).

    • Related Report
      2003 Annual Research Report
  • [Publications] A.Gendiar: "Stable Optimization of Tensor Product Variational Functions"Prog.Theor.Phys.. 110. 691-699 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] K.Higashijima: "Three-dimensional nonlinear sigma models in the Wilsonian renormalization method"Prog.Theor.Phys.. 110. 563-578 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] 斯波 弘行: "相互作用する電子(岩波「物理の世界」シリーズ)"岩波書店. 80 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] Hidenori Sonoda: "Bootstrapping perturbative perfect actions"Physical Review D. 67(To be published). (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] A.Gendiar, T.Nishino: "Latent heat observation of the q=3,4, and 5 Potts models by tensor product variational approach"Physical Review E. 65. 46702 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] A.Kemper, A.Gendiar, T.Nishino, A.Schadschnider, J.Zittartz: "Stochastic light-cone CTMRG : a new DMRG approach to stochastic models"J. Phys. A : Math. Gen.. 36. 29-41 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] E.Kaneshita, M.Ichioka, K.Machida: "Study of phonon anomalies in stripe phase of high Tc cuprates"Physical B. (To be published).

    • Related Report
      2002 Annual Research Report
  • [Publications] Shigenori Seki: "D5-brane in anti-de Sitter space and Penrose limit"Phys. Lett. B. 542. 165-170 (2002)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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