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

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1.Correlation function of XXZ chain at ground stateAt (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 fieldUsing 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 interactionIn 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.