2005 Fiscal Year Final Research Report Summary
Theoretical and Numerical Study of Many-Body Interaction and Quantum Phase Transition in Low-Dimensional Magnets
| Project/Area Number |
14340099
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
固体物性Ⅱ(磁性・金属・低温)
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| Research Institution | University of Tokyo |
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Principal Investigator |
TAKAHASHI Minoru University of Tokyo, Institute for Solid State Physics, Professor, 物性研究所, 教授 (40029731)
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| 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)
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| Project Period (FY) |
2002 – 2005
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| Keywords | Low-Dimensional Systems / Spin Systems / Exact Solution / Bethe ansatz / Correlation Function / Thermodynamics / Exact diagonalization / Magnetization curve |
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| 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.
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