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Theoretical and Numerical Study of Many-Body Interaction and Quantum Phase Transition in Low-Dimensional Magnets

Research Project

Project/Area Number 14340099
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field 固体物性Ⅱ(磁性・金属・低温)
Research InstitutionUniversity of Tokyo

Principal Investigator

TAKAHASHI Minoru  University of Tokyo, Institute for Solid State Physics, Professor, 物性研究所, 教授 (40029731)

Co-Investigator(Kenkyū-buntansha) SHIROISHI Masahiro  University of Tokyo, Institute for Solid State Physics, Research Associate, 物性研究所, 助手 (80323632)
SAKAI Toru  Japan Atomic Energy Agency, 量子ビーム応用研究部門, 研究主幹 (60235116)
Project Period (FY) 2002 – 2005
Project Status Completed (Fiscal Year 2005)
Budget Amount *help
¥8,400,000 (Direct Cost: ¥8,400,000)
Fiscal Year 2005: ¥1,600,000 (Direct Cost: ¥1,600,000)
Fiscal Year 2004: ¥2,500,000 (Direct Cost: ¥2,500,000)
Fiscal Year 2003: ¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2002: ¥2,800,000 (Direct Cost: ¥2,800,000)
KeywordsLow-Dimensional Systems / Spin Systems / Exact Solution / Bethe ansatz / Correlation Function / Thermodynamics / Exact diagonalization / Magnetization curve / 相関関数
Research Abstract

1.Correlation function of XXZ chain at ground state
At (Δ=1) of spin 1/2 XXZ chain, 2-point correlation function is known only at nearest and next nearest one is known by (Hulthen, 1938) and (Takahashi, 1977).
<S^z_j=S^z_<j+1>>=1/(12)-1/3ln2,<S^z_jS^z_<j+2>>=1/(12)-4/3ln2+3/4ζ(3) In this project we obtain the third neighbor correlator
<S^z_jS^z_<j+3>=1/(12)-3ln2+(37)/6ζ(3)-(14)/3ln2・ζ(3)-3/2ζ^2(3)-(125)/(24)ζ(5)+(25)/3ln2・ζ(5). Moreover we develop this calculation and obtain analytic expression up to seventh correlator.
2.Dynamical structure factor of XXZ chain under magnetic field
Using determinant expression of form factor of local operators, we calculated dynamical structure factor S_<μμ>(q,ω)=2πΣ__λ|<GS|S^μ_q|λ>|^2δ(ω-ω_λ)at critical region (-1<Δ【less than or equal】1)in the magnetic field.
3.Magnetic field induced quantum phase transition of spin-ladder system with ring-exchange interaction
In strongly correlated electron systems with plaquette like spin ladder system or square lattice, there exists four-spin exchange interaction which is called ring-exchange interaction. We treat Heisenberg spin-ladder. We analyze the field induced phase transition which is caused by ring interaction using numerical diagonalization, finite-size scaling and degenerate perturbation theory.

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

    (35 results)

All 2005 2004 2003 Other

All Journal Article (23 results) Publications (12 results)

  • [Journal Article] Experimental Observation of the 1/3 Magnetization Plateau in a Diamond Chain Compound Cu_3 (CO_3)_2 (OH)_22005

    • Author(s)
      H.Kikuchi, Y.Fujii, M.Chiba, S.Mitsudo, T.Idehara, T.Tonegawa, K.Okamoto, T.SakaiT.Kuwai, H.Ohta
    • Journal Title

      Phys. Rev. Lett. 94

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] First principle approach to correlation functions of spin-1/2 Heisenberg chain : forth-neighbor correlators2005

    • Author(s)
      H.E.Boos, M.Shiroishi, M.Takahashi
    • Journal Title

      Nucl.Phys.B 712

      Pages: 573-599

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Experimental Observation of the 1/3 Magnetization Plateau in a Diamond Chain Compound Cu_3(CO_3)_2(OH)_22005

    • Author(s)
      H.Kikuchi, Y.Fujii, M.Chiba, S.Mitudo, T.Idehara, T.Tonegawa, K.Okamoto, T.Sakai, T.Kuwai, H.Ohta
    • Journal Title

      Phys.Rev.Lett. 94

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Exact calculation of correlation functions for spin-1/2 Heisenberg chain2005

    • Author(s)
      M.Shiroishi, M.Takahashi
    • Journal Title

      J.Phys.Soc.Jpn.Suppl. 74

      Pages: 47-52

    • Related Report
      2005 Annual Research Report
  • [Journal Article] High temperature expansion of emptiness formation probability for isotropic Heisenberg chain2005

    • Author(s)
      Z.Tsuboi, M.Shiroishi
    • Journal Title

      J.Phys.A : Math.Gen. 38

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Correlation functions of the spin-1/2 anti-ferromagnetic Heisenberg chain : exact calculation via the generating functions2005

    • Author(s)
      J.Sato, M.Shiroishi, M.Takahashi
    • Journal Title

      Nucl.Phys.B 729

      Pages: 441-466

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Impurity Pinning of Spin Density Wave2005

    • Author(s)
      T.Sakai
    • Journal Title

      Prog.Theor.Phys.Suppl. 157

      Pages: 148-151

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Field-Induced Incommensurate Order in Spin Ladder with Ring Exachange.2005

    • Author(s)
      T.Sakai, K.Okamoto
    • Journal Title

      J.Phys.Chem.Solid 66

      Pages: 1450-1453

    • Related Report
      2005 Annual Research Report
  • [Journal Article] Quantum phase transitions of spin chiral nanotubes2005

    • Author(s)
      M.Matsumoto, T.Sakai, M.Sato, H.Takayama, S.Todo
    • Journal Title

      Physica E 29

      Pages: 660-663

    • Related Report
      2005 Annual Research Report
  • [Journal Article] First principle approach to correlation functions of spin-1/2 Heisenberg chain : fourth-neighbor correlators2005

    • Author(s)
      H.E.Boos, M.Shiroishi, M.Takahashi
    • Journal Title

      Nucl.Phys.B (印刷中)

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Nonlinear integral equations for thermodynamics of the $U_{q} (widehat{sl(r+1)}$ Perk-Schultz model2005

    • Author(s)
      Z.Tsuboi, M.Takahashi
    • Journal Title

      J.Phys.Soc.Jpn Vol.74 No.3

      Pages: 898-904

    • NAID

      210000105909

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Next Nearest Neighbor Correlation Functions of thi Spin-1/2 XXZ Chain at Massive Region2004

    • Author(s)
      M.Takahashi, G.Kato, M.Shiroishi
    • Journal Title

      J.Phys.A 37

      Pages: 5097-5123

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Evaluation of Dynamic Spin Structure Factor for the Spin-1/2 XXZ chain in a Magnetic Field2004

    • Author(s)
      J.Sato, M.Shiroishi, M.Takahashi
    • Journal Title

      J. Phys. Soc. Jpn. 73

      Pages: 3008-3014

    • NAID

      110001979249

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Frustration-induced eta inversion in the S=1/2 bond-alternating spin chain2004

    • Author(s)
      N.Maeshima, K.Okunishi, K._Okamoto, T._Sakai
    • Journal Title

      Phys.Rev. Lett. 93

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] First principle approach to correlation functions of spin-1/2 Heisenberg chain : forth-neighbor correlators2004

    • Author(s)
      H.E.Boos, M.Shiroishi, M.Takahashi
    • Journal Title

      Nucl. Phys. B 712

      Pages: 573-599

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Evaluation of Dynamic Spin Structure Factor for the Spin-1/2 XXZ chain in a Magnetic Field2004

    • Author(s)
      J.Sato, M.Shiroishi, M.Takahashi
    • Journal Title

      J.Phys.Soc.Jpn. 73

      Pages: 3008-3014

    • NAID

      110001979249

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Frustration-induced eta inversion in the S=1/2 bond-alternating spin chain2004

    • Author(s)
      N.Maeshima, K.Okunishi, K.Okamoto, T.Sakai
    • Journal Title

      Phys.Rev.Lett. 93

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Third-neighbour and other four-point correlation functions of spin-1/2 XXZ chain2004

    • Author(s)
      G.Kato, M.Shiroishi, M.Takahashi, K.Sakai
    • Journal Title

      J.Phys.A Math.Gen.37

      Pages: 5097-5123

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Evaluation of Dynamic Spin Structure Factor for the Spin-1/2 XXZ Chain in a Magnetic Field2004

    • Author(s)
      J.Sato, M.Shiroishi, M.Takahashi
    • Journal Title

      J.Phys.Soc.Jpn. 73

      Pages: 3008-3014

    • NAID

      110001979249

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Frustration-induced eta inversion in the S=1/2 bond-alternating spin chain2004

    • Author(s)
      N.Maeshima, K.Okunishi, K.Okamoto, T.Sakai
    • Journal Title

      Phys.Rev.Letters 93

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Anomalous magnetization process in frustrated spin ladders2004

    • Author(s)
      T.Sakai, K.Okamoto, K.Okunishi, M.Sato
    • Journal Title

      J.Phys.Condens.Matter. 16

      Pages: 785-789

    • Related Report
      2004 Annual Research Report
  • [Journal Article] Third Neighbor Correlators of Spin-1/2 Heisenberg Antiferromagnet2003

    • Author(s)
      K.Sakai, M.Shiroishi, Y._Nishiyama, _M._Takahashi
    • Journal Title

      Phys. Rev. E67

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Journal Article] Third Neighbor Correlators of Spin-1/2 Heisenberg Antiferromagnet2003

    • Author(s)
      K.Sakai, M.Shiroishi, Y.Nishiyama, M.Takahashi
    • Journal Title

      Phys.Rev.E 67

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2005 Final Research Report Summary
  • [Publications] K.Sakai, M.Shiroisi, Y.Nishiyama, M.Takahashi: "Third Neighbor Correlators of Spin-1/2 Heisenberg Antiferromagnet"Phys.Rev.E. 67. 065101(R)1-065101(R)4 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Takahashi: "Thermodynamics and Correlation Functions of XXZ Chain"Czechoslovak Journal of Physics. 53. 1125-1130 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Takahashi, G.Kato, M.Shiroishi: "Next Nearest Neighbor Correlation Functions of the Spin-1/2 XXZ Chain at Massive Region"J.Phys.Soc.Jpn.. 73. 245-253 (2004)

    • Related Report
      2003 Annual Research Report
  • [Publications] A.Kluemper, K.Sakai: "The thermal conductivity of the spin-1/2 XXZ chain at arbitrary temperature"J.Phys.A. Math.Gen.35. 2173-2182 (2002)

    • Related Report
      2003 Annual Research Report
  • [Publications] T.Sakai, N.Okazaki, K.Okamoto, K.Kindo, Y.Narumi, Y.Hosokosi K.kato, K.Inoue, T.Goto: "Magnetization plateaus in S=1 spin ladder"phys.stat.sol.. 236. 429-432 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.T.Batchelor, X.W.Guan, N.Oelkers, K.Sakai, Z.Tsuboi, A.Foerster: "Exact results for the thermal and magnetic properties of strong coupling ladder compounds"Physical Review Letters. Vol.91,No.21. 217202-1-217202-4 (2003)

    • Related Report
      2003 Annual Research Report
  • [Publications] M.Shiroishi, M.Takahashi: "Integral Equation Generates High-Temperature Expansion of the Heisenberg Chain"Physical Review Letters. 89,No.11. 117201-1-117201-4 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] H.E.Boos, V.E.Korepin, Y.Nishiyama, M.Shiroishi: "Quantum correlations and number theory"Journal of Physics A : Mathematical and General. 35. 4443-4451 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] M.Takahashi, M.Shiroishi: "Thermodynamic Bethe ansatz equations of one-dimensional Hubbard model and high-temperature expansion"Physical Review B. 65. 165104-1-165104-9 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] T.Sakai, M.Takahashi: "Spin flop in 1D quantum antiferromagnets"Prog.Theor.Phys.. Suppl.No.145. 125-129 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] S.Yamamoto, T.Sakai, A.Koga: "Re-Entrant Quantum Phase Transitions in Antiferromagnetic Spin-1 Ladders"J.Phys.Soc.Jpn.. 71. 1250-1253 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] A.Klumper, K.Sakai: "The thermal conductivity of the spin-1/2 XXZ chain at arbitrary temperature"J.Phys.A : Math.Gen. 35. 2173-2182 (2002)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2020-05-15  

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