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

低维磁体中多体相互作用和量子相变的理论与数值研究

• 批准号: 14340099
• 负责人: TAKAHASHI Minoru
• 金额: $ 5.38万
• 依托单位: University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2002
• 资助国家: 日本
• 起止时间: 2002 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14340099/
• 关键词: Low-Dimensional Systems; Spin Systems; Exact Solution; Bethe ansatz; Correlation Function; Thermodynamics; Exact diagonalization; Magnetization curve; 相関関数

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.

1.XXZ链基态关联函数在自旋1/2的XXZ链中，两点关联函数仅在最近点已知，次最近点关联函数已知(Hulten，1938)和(Takahashi，1977).&lt；S^z_j=S^z_&lt；j+1&gt；&gt；=1/(12)-1/3ln2，&lt；S^z_jS^z_&lt；j+2&gt；&gt；=1/(12)-4/3ln2+3/4ζ(3))在本项目中，我们得到了第三邻相关器&lt；S^z_js^z_&lt；j+3&gt；=1/(12)-3ln2+(37)/6ζ(3)-(14)/3ln2・ζ(3)-3/2ζ^2(3)-(125)/(24)ζ(5)+(25)/3ln2・ζ(5).利用局域算符形状因子的行列式表达式，计算了临界区(-1&lt；μμ&gt；(q，ω)=2πΣ__λ|&lt；GS|S^μ_q|λ&gt；|^2δ(ω-ω_λ)的动态结构因子。Δ[小于或等于]1)。3.磁场诱导具有环交换作用的自旋梯形系统的量子相变在具有斑块状自旋梯形系统或正方形晶格的强关联电子系统中，存在四自旋交换相互作用，称为环交换相互作用。我们对待海森伯格的自旋梯。我们用数值对角化、有限尺寸标度和简并微扰理论分析了环相互作用引起的场诱导相变。

项目成果

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)

M.Takahashi、G.Kato、M.Shiroishi：“大规模区域自旋 1/2 XXZ 链的下一个最近邻相关函数”J.Phys.Soc.Jpn.. 73. 245-253 (2004)

Third-neighbour and other four-point correlation functions of spin-1/2 XXZ chain

• DOI: 10.1088/0305-4470/37/19/001
• 发表时间: 2004-05-14
• 期刊: JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL
• 作者: Kato, G;Shiroishi, M;Sakai, K
• 通讯作者: Sakai, K

Quantum phase transitions of spin chiral nanotubes

自旋手性纳米管的量子相变

• 发表时间: 2005
• 期刊: PHysica E 29
• 作者: Y. Hiyashimizu;K. Sensui;J.Osiecki;Y. Hayakawa;A. Kasuya;A. Chiba;A. Natori and S. Suto;堀川 裕加;M.Matsumoto
• 通讯作者: M.Matsumoto

High temperature expansion of emptiness formation probability for isotropic Heisenberg chain

各向同性海森堡链空洞形成概率的高温展开

• 发表时间: 2005
• 期刊: J.Phys.A : Math.Gen. 38
• 作者: Z.Tsuboi;M.Shiroishi
• 通讯作者: M.Shiroishi

Frustration-induced eta inversion in the S=1/2 bond-alternating spin chain

S=1/2 键交替自旋链中受挫诱导的 eta 反转

• 发表时间: 2004
• 期刊: Phys.Rev. Lett. 93
• 作者: N.Maeshima;K.Okunishi;K._Okamoto;T._Sakai
• 通讯作者: T._Sakai