Theoretical study of one-dimensional quantum spin sustems : q in which two kinds of spins are arranged alternatively

一维量子自旋体系的理论研究：两种自旋交替排列的q

• 批准号: 09640464
• 负责人: TONEGAWA Takashi
• 金额: $ 1.92万
• 依托单位: KOBE UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 1998
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09640464/
• 关键词: quantum mixed spin chain; ground-state phase diagram; thermodynamic properties; DMRG method; valence-bond-solid picture; two-spin correlation function; string correlation function; quantum monte Carlo method; 1次元量子スピン系; 規則混合系; 有限系の厳密対角化法; 基底状態相

We have investigated both analytically and numerically the ground-state and thermodynamic properties of the quantum mixed spin-1/2-1/2-1-1 chain described by the Hamiltonian H = ΣィイD31N/4(/)l=1ィエD3(JィイD21ィエD2・SィイD4→ィエD4ィイD24l-3ィエD2・sィイD4→ィエD4ィイD24l-2ィエD2 + JィイD22ィエD2 sィイD4→ィエD4ィイD24l-2ィエD2・SィイD4→ィエD4ィイD24l-1ィエD2 + JィイD23ィエD2 SィイD4→ィエD4ィイD24l-1ィエD2・SィイD4→ィエD4ィイD24lィエD2 + JィイD22ィエD2 SィイD4→ィエD4ィイD24lィエD2・sィイD4→ィエD4ィイD24l+1ィエD2), where two S = 1/2 spins (sィイD4→ィエD4ィイD24l-3ィエD2 and sィイD4→ィエD4ィイD24l-2ィエD2) and two S = 1 spins (SィイD4→ィエD4ィイD24l-1ィエD2 and ィイD4→ィエD4ィイD24lィエD2 are arrayed alternatively.In several limiting cases of JィイD21ィエD2, JィイD22ィエD2, and JィイD23ィエD2 we have applied the Wigner-Eckart theorem and carried out a perturbation calculation to examine the behaviors, in these cases, of the massless lines where the energy gap vanishes. Guided by these results, we have performed a density-matrix renormalization-group calculation to determine in detail the ground-state phase diagram on t … More he JィイD21ィエD2 versus JィイD22ィエD2 plane with JィイD23ィエD2 = 1.0. From the gapless points of the singlet-triplet energy gap, five boundary lines have been determined, which divide the phase diagram into six regions. In three regions the ground states with the Haldane-phase character appear, while in the remaining three regions those with the dimer character appear. We have also presented a characterization of the phases concerning how the ground state in each phase is represented in the framework of the valence-bond-solid (VBS) picture. Making use of the matrix-product wave function, we have classified the VBS pictures and interpreted the ground-state phase diagram in terms of symmetries schematically related to the VBS pictures. We have investigated the ground-state nearest-neighboring two-spin correlation functions and a kind of string order parameters, by which we have confirmed the validity of the characterization.Furthermore, we have carried out a quantum Monte Carlo calculation which takes the global flips along the Trotter direction into account to elucidate the temperature dependences of the specific heat and the magnetic susceptibility. In particular, we have found that the specific heat per unit cell versus temperature curve for JィイD22ィエD2 = 5.0 with JィイD21ィエD2 = JィイD23ィエD2 = 1.0 has a double peak. Less

我们已经在分析和数值上研究了由哈密顿量H =σiiD31N/4（/）L = 1E D3所描述的量子混合旋转旋转1/2-1/2-1-1链的链（JII D21E D21E D21E D2 d4 d4 d4→EE D4D22224L-l-3e d4 d4） D2 + JII D22E D2 SII D4→EE D4D24L-2E D2 d2 sii D4→EE D4D24L-1E D2 + JII D2 + JII D2 d2 d2 s = 1/2 spins = 1/2 Spins（SY D4→sy D24L-1 SPY D2，YE D2，YE D4→YE D4→YE D24→YE D24L-1L-1间谍D2和Ye d4→Ye D24L+1间谍D2），其中两个S = 1 spin（SY D4→YE D4 D24L-3 SPY D2和YE D4→YE D4→YE D4 D24L-2 SPY）和两个S = 1 s = 1个旋转或者，在几个有限的案例中，JII D21，JII D22和JII D23 D2我们应用了Wigner-Eckart理论，并进行了扰动计算，以检查这些情况下的无数群体，在这些情况下，在这些群体中逐渐消失了。在T…更多HE HE JII D21，JII D2与JII D22，D2平面具有JII D23E D2 = 1.0。从单三个三元素能隙的无间隙点，已经确定了五个边界线，将相图划分为六个区域。在三个区域中，基态具有haldane-相相的外观，而在其余三个区域中，那些具有二聚体特征外观的区域。我们还介绍了有关在价值 - 键 - 固体（VBS）图片框架中如何表示每个阶段基态的阶段的表征。利用矩阵产物波函数，我们已将VBS图片分类，并用与VBS图片示意性相关的对称性来解释地面相图。我们已经调查了接地的邻居两旋旋转相关函数和一种弦顺序参数，通过该参数，我们已经确认了表征的有效性。Furthermore，我们已经执行了量子蒙特卡洛计算，该计算将沿着trot的全局瓣沿trot方向带入了磁力方向，以考虑到特定的热量和特定的磁性强度。特别是，我们发现JII D22 = 5.0的每个单位电池与温度曲线的特异性热量与JII D21 = JII D23 E D2 = 1.0具有双峰。较少的

项目成果

Shigeyoshi Mori: "Dynamic Spin Correlation Function of the Alternating Spin-1/2 Antiferromagnetic chain with Competing Interactions"Journal of the Physical Societyof Japan. 67. 1409-1415 (1998)

Shigeyoshi Mori：“具有竞争相互作用的交替自旋 1/2 反铁磁链的动态自旋相关函数”日本物理学会杂志。

T. Tonegawa, T. Hikihara, T. Nishino, M. kaburagi, S. Miyashita and H.-J. Mikeska: "One-Dimensional Heisen-berg Antiferromagnet in which Two S = 1/2 and Two S = 1 Spins Are Arranged Alternatively"J. Magn. Magn. Mater.. 177-181. 647-649 (1998)

T.利根川、T.Hikihara、T.西野、M.kaburagi、S.Miyashita 和 H.-J。

Takashi Tonegawa: "One-Dimentional Heisenberg Antiteeromagnet in which Two S=1/2 and Two S=1 Spins are Arranged Alternatively"Journal of Magnetism and Magnetic Materials. 177-181. 647-649 (1998)

利根川隆：“一维海森堡反磁体，其中两个 S=1/2 和两个 S=1 自旋交替排列”《磁性与磁性材料杂志》。

T. Hikihara, T. Tonegawa, M. Kaburagi, T. Nishino, Seiji Miyashita and H.-J. Mikeska: "Ground-State Phase Diagram of the Spin-l/2-1/2-1-1 Chain"(preprint).

T. Hikihara、T. Tonekawa、M. Kaburagi、T. Nishino、Seiji Miyashita 和 H.-J。

Takashi Tonegawa: "Ground-State Magnetization Curve of a Generalized Spin-1/2 Ladder" Physica B. (1998)

Takashi Tonekawa：“广义自旋 1/2 梯的基态磁化曲线”Physica B. (1998)